update: February 6, 2020

The 15th East Asian Conference onGeometric Topology

February 10–13, 2020
RIMS, Kyoto University, Japan
http://www.kurims.kyoto-u.ac.jp/~eacgt/

The 15th East Asian Conference onGeometric Topology
February 10–13, 2020
RIMS, Kyoto University, Japan

Program Committee :Hyungryul Baik (KAIST), Jae Choon Cha (POSTECH),
Seiichi Kamada (Osaka University), Sang-hyun Kim (Seoul National University),Toshitake Kohno (University of Tokyo), Yi Liu (Peking University),
Tomotada Ohtsuki (RIMS, Kyoto University),
Ruifeng Qiu (East China Normal University), Jiajun Wang (Peking University),
Ying Zhang (Soochow University)

Founding Members :Boju Jiang (Peking University), Gyo Taek Jin (KAIST),
Mitsuyoshi Kato (Kyushu University), Akio Kawauchi (Osaka City University),
Ki Hyoung Ko (KAIST), Yukio Matsumoto (Gakushuin University),
Shicheng Wang (Peking University)

Organizing Committee :Tetsuya Abe, Kazuo Habiro, Ayumu Inoue, Katsumi Ishikawa,
Tetsuya Ito, Tomotada Ohtsuki (chair), Narutaka OzawaiWelcome to
The 15th East Asian Conference on Geometric Topology
February 10–13, 2020
RIMS, Kyoto University, Japan
http://www.kurims.kyoto-u.ac.jp/~eacgt/
Welcome to RIMS, Kyoto University, Japan. The purpose of the conference is to help
promoting the academic exchange and the friendship among researchers of three East
Asian countries in the area of geometric topology and encouraging graduate studentsof the three countries to study in this fascinating area of mathematics.
This conference is supported by the following:
Research Institute for Mathematical Sciences, Kyoto University
JSPS, Grant-in-Aid for Scientific Research (S) : JP15H05739
JSPS, Grant-in-Aid for Scientific Research (A) : JP16H02145
JSPS, Grant-in-Aid for Scientific Research (B) : JP18H01119
JSPS, Grant-in-Aid for Scientific Research (B) : JP19H01788
JSPS, Grant-in-Aid for Scientific Research (C) : JP18K03306
JSPS, Grant-in-Aid for Scientific Research (C) : JP19K03490
JSPS, Grant-in-Aid for Exploratory Research : JP16K13754
JSPS, Grant-in-Aid for Exploratory Research : JP19K21830
We hope you will enjoy the conference.

Tomotada Ohtsuki
Chair

ii

Contents
1.
2.
3.
4.
5.

1
2
4
11
29

Information
Talk Schedule
Program
Abstracts
Campus Map

iii

1. Information
Lecture rooms:
The plenary talks are given at Room 420 on the 4th floor. Parallel sessions take placein 3 rooms: Room 420, Room 111 and Room 110 (both Rooms 111 and 110 are on
the 1st floor).
Registration:
When you arrive at the conference, please input your information (name, aﬃliationand email address) at one of the terminals at the backside of Rooms 420, 111 and 110.
Furthermore, please take your name card and a copy of the booklet at the entranceof Room 420 (in front of the room or in the room).
To participants from China and Korea: Please go to Room 103 on the 1st floor at
13:00–14:00 on February 10th (Monday) to make the procedure of your visit. If
you can not visit there at that time, please go to Room 104 (International Research
Support Oﬃce (RIMS secretary)) on the 1st floor when you arrive at the conference.
To participants who attend banquets and/or excursion: Please go to Room 103 on the
1st floor at 13:00–14:00 on February 10th (Monday) to confirm your attendance ofbanquets and/or excursion. If you can not visit there at that time, please contact a
local organizer when you arrive at the conference.
Internet connection:
The eduroam wireless network is available on site. If you have some problems related
to eduroam, please contact your home institution’s technical support.
Banquets:
We have banquets in the cafe restaurant Camphora at 17:00 on February 10th (Monday) and at 19:00 on February 13th (Thursday). We ask the participants of thebanquets to go there at that time. For the location of Camphora, please see the map
at the end of this booklet.
We ask the participants of the conference to arrange the other meals by yourself.
Excursion:
We have an excursion in the afternoon on February 13th (Thursday). We ask theparticipants of the excursion to go to the entrance of RIMS at 13:00 on February 13th
(Thursday).
For further information, please see the conference web page:
http://www.kurims.kyoto-u.ac.jp/~eacgt/
12. Talk Schedule
February 10 (Monday)
Chair
9:50–10:30
10:50–11:30

Room 420 (live streaming are available at Rooms 111 and 110)
Kazuo Habiro
Qingtao Chen
Kokoro Tanaka

11:30–13:00

Lunch

13:00–14:00

Room 103
Registration

Chair
14:00–14:20
14:25–14:45

Room 420
Shin SatohGyo Taek Jin
Seungsang Oh

Room 111
Jae Choon Cha
Ayumu Inoue
Min Hoon Kim

Room 110
Toshie Takata
Marco De Renzi
Hiroaki Karuo

Jun UekiTakefumi Nosaka

Daiki Iguchi
Naoko Kamada

Room 111
Wataru Yuasa
Ryoto Tange
Marı́a de los Angeles
Guevara Hernández
Eiko Kin

Room 110
Naoko Kamada
Yuta Taniguchi
Xinghua Gao

Kazuhiro Ichihara
Ken’ichi Yoshida
BoGwang Jeon

Masaaki Suzuki
Hyungkee Yoo
Tomo Murao

14:45–15:15 Tea Time
15:15–15:35 Seokbeom Yoon
15:40–16:00 Jung Hoon Lee
17:00–19:00 Banquet

February 11 (Tuesday)
Chair
13:00–13:20
13:25–13:45

Room 420
Kazuto Takao
Katsumi Ishikawa
Kyungbae Park

13:50–14:10

Shin Satoh(blank)14:10–14:40 Tea Time
Chair
Yasutaka Nakanishi
14:40–15:00 Benjamin Bode
15:05–15:25 Seiichi Kamada

2February 12 (Wednesday)
Chair
9:50–10:30
10:50–11:30

Room 420 (live streaming are available at Rooms 111 and 110)
Seiichi Kamada
Taehee Kim
Takahiro Oba

11:30–13:00

Lunch

Chair
13:00–13:20
13:25–13:45
13:50–14:10

Room 420
Tatsuro Shimizu
Kazuhiro Ichihara
Anderson Vera
Delphine Moussard

Room 111
Katsumi Ishikawa
Wataru Yuasa
Airi Aso
Hideo Takioka

Room 110
Eiko Kin
Yuka Kotorii
Shosaku Matsuzaki
Robert Tang

Hirotaka Akiyoshi
Nobutaka Asano
Kazuto Takao

Takahiro Oba
Takuya Katayama
Donggyun Seo

14:10–14:40 Tea Time
Chair
Tetsuya Ito
14:40–15:00 Sungkyung Kang
15:05–15:25 Jae Choon Cha

February 13 (Thursday)
Chair
9:50–10:30
10:50–11:30

Room 420 (live streaming are available at Rooms 111 and 110)
Taizo Kanenobu
Toshie Takata
Inkang Kim

11:30–13:00
13:00–19:00
19:00–21:00

Lunch
Excursion
Banquet33. ProgramFebruary 10 (Monday)
ROOM 420 (live streaming are available at Rooms 111 and 110)Chair: Kazuo Habiro
9:50–10:30 Qingtao Chen (New York University Abu Dhabi)
Recent development of volume conjectures
10:50–11:30 Kokoro Tanaka (Tokyo Gakugei University)
Independence of Roseman moves for surface knots
ROOM 103
13:00–14:00

Registration

ROOM 420
Chair: Shin Satoh
14:00–14:20 Gyo Taek Jin (KAIST)
Minimal grid diagrams of 11 crossing prime alternating knots
14:25–14:45 Seungsang Oh (Korea University)
Quantum knot mosaics and bounds of the growth constant
15:15–15:35 Seokbeom Yoon (KIAS)
Adjoint Reidemeister torsions from wrapped M5-branes
15:40–16:00 Jung Hoon Lee (Jeonbuk National University)
On Casson–Gordon’s rectangle condition for 3-bridge decompositions of knots
ROOM 111
Chair: Jae Choon Cha
14:00–14:20 Ayumu Inoue (Tsuda University)
The fibered knots whose knot quandles are finite
14:25–14:45 Min Hoon Kim (POSTECH)
Non-slice linear combinations of algebraic knots
15:15–15:35 Jun Ueki (Tokyo Denki University)
Profinite rigidity for twisted Alexander invariants
15:40–16:00 Takefumi Nosaka (Tokyo Institute of Technology)
K1 -valued Alexander polynomials of knots

4ROOM 110Chair: Toshie Takata
14:00–14:20 Marco De Renzi (Waseda University)
2 + 1-TQFTs from non-semisimple modular categories
14:25–14:45 Hiroaki Karuo (RIMS, Kyoto University)
On the reduced Dijkgraaf–Witten invariant of knots in the Bloch group of Fp
15:15–15:35 Daiki Iguchi (Hiroshima University)
The Goeritz groups of bridge decompositions
15:40–16:00 Naoko Kamada (Nagoya City University)
On almost classical virtual links
17:00–19:00

Banquet5February 11 (Tuesday)
ROOM 420
Chair: Kazuto Takao
13:00–13:20 Katsumi Ishikawa (RIMS, Kyoto University)
Vanishing of open Jacobi diagrams with odd legs
13:25–13:45 Kyungbae Park (Seoul National University)
On definite fillings of lens spaces
13:50–14:10 Shin Satoh (Kobe University)
The 2-knots of triple point number four
Chair: Yasutaka Nakanishi
14:40–15:00 Benjamin Bode (Osaka University)
Knotted surfaces as algebraic varieties
15:05–15:25 Seiichi Kamada (Osaka University)
The motion group and the ring group of an H-trivial link and its application
ROOM 111
Chair: Wataru Yuasa
13:00–13:20 Ryoto Tange (Tokyo Denki University)
Non-acyclic SL2 -representations of twist knot groups and (−3)-Dehn surgeries
13:25–13:45 Marı́a de los Angeles Guevara Hernández (Osaka City University)
The braid alternation number and the braid dealternating number
13:50–14:10 Eiko Kin (Osaka University)
Problem on pseudo-Anosov minimal entropies
Chair: Kazuhiro Ichihara
14:40–15:00 Ken’ichi Yoshida (Saitama University)
Degeneration of 3-dimensional hyperbolic cone structures with decreasingcone angles
15:05–15:25 BoGwang Jeon (POSTECH)
Rigidity in hyperbolic Dehn fillings

6ROOM 110Chair: Naoko Kamada
13:00–13:20 Yuta Taniguchi (Osaka City University)
Quandle coloring quivers for links and quivers of quandles
13:25–13:45 Xinghua Gao (KIAS)
Orderability of Dehn fillings and the L-space conjecture
13:50–14:10 (blank)
Chair: Masaaki Suzuki
14:40–15:00 Hyungkee Yoo (Korea University)
Small lattice spatial 3-regular graphs with two vertices
15:05–15:25 Tomo Murao (University of Tsukuba)
Disk systems for handlebody-knots and their isotopy classes

7February 12 (Wednesday)
ROOM 420 (live streaming are available at Rooms 111 and 110)Chair: Seiichi Kamada
9:50–10:30 Taehee Kim (Konkuk University)
Primary decomposition in knot concordance
10:50–11:30 Takahiro Oba (RIMS, Kyoto University)
Lefschetz–Bott fibrations and their applications to symplectic geometry
ROOM 420
Chair: Tatsuro Shimizu
13:00–13:20 Kazuhiro Ichihara (Nihon University)
Two-bridge knots admit no purely cosmetic surgeries
13:25–13:45 Anderson Vera (RIMS, Kyoto University)
Johnson-type homomorphisms and the Le–Murakami–Ohtsuki invariant
13:50–14:10 Delphine Moussard (Aix-Marseille University)
Three-dimensional characterization of the slice genus of knots and links
Chair: Tetsuya Ito
14:40–15:00 Sungkyung Kang (Chinese University of Hong Kong)
Link homology theories and ribbon concordances
15:05–15:25 Jae Choon Cha (POSTECH)
Primary decomposition in low dimensional topology
ROOM 111
Chair: Katsumi Ishikawa
13:00–13:20 Wataru Yuasa (RIMS, Kyoto University)
The sl3 colored Jones polynomial of a (2, m)-torus link and its tail13:25–13:45 Airi Aso (Tokyo Metropolitan University)
Twisted Alexander polynomials of tunnel number one Montesinos knots
13:50–14:10 Hideo Takioka (Kyoto University)
Vassiliev knot invariants derived from cable Γ-polynomials
Chair: Hirotaka Akiyoshi
14:40–15:00 Nobutaka Asano (Tohoku University)
Vertical 3-manifolds in simplified genus 2 trisections of 4-manifolds
15:05–15:25 Kazuto Takao (Kyoto University)
Local theory of the graphic of two trisections of a 4-manifold

8ROOM 110Chair: Eiko Kin
13:00–13:20 Yuka Kotorii (RIKEN)
Levine’s classification of 4-component links up to link-homotopy and its
classification by claspers
13:25–13:45 Shosaku Matsuzaki (Takushoku University)
Oriented surfaces in the 3-sphere and their coloring invariants
13:50–14:10 Robert Tang (OIST)
Coarse and fine geometry of the saddle connection graph
Chair: Takahiro Oba
14:40–15:00 Takuya Katayama (Hiroshima University)
Embeddability between the right-angled Artin groups of surfaces
15:05–15:25 Donggyun Seo (Seoul National University)
Dehn twists, right-angled Artin subgroups and trees

9February 13 (Thursday)
ROOM 420 (live streaming are available at Rooms 111 and 110)Chair: Taizo Kanenobu
9:50–10:30 Toshie Takata (Kyushu University)
The strong slope conjecture for cablings and connected sums
10:50–11:30 Inkang Kim (KIAS)
New way of constructing mapping class group invariant Kähler metrics on
Teichmüller space and the convexity of energy function
13:00–19:00
19:00–21:00

Excursion
Banquet10

4. Abstracts
Plenary talks
Qingtao Chen New York University Abu Dhabi
Title: Recent development of volume conjectures
Abstract: The original Volume Conjecture of Kashaev–Murakami–Murakami predicts a precise relation between the asymptotics of the colored Jones polynomials ofa knot in S 3 and the hyperbolic volume of its complement.
I will discuss two diﬀerent directions that lead to generalizations of this conjecture.
The first direction concerns diﬀerent quantum invariants of knots, arising from thecolored SU (n) (with the colored Jones polynomial corresponding to the case n = 2).
I will first display subtle relations between congruence relations, cyclotomic expansions and the original Volume Conjecture for colored Jones polynomials of knots. I
will then generalize this point of view to the colored SU (n) invariant of knots. Certain congruence relations for colored SU (n) invariants, discovered in joint work with
K. Liu, P. Peng and S. Zhu, lead us to formulate cyclotomic expansions and a Volume Conjecture for these colored SU (n) invariants. I will also discuss similar ideas
for the superpolynomials that arise in HOMFLY–PT homology. In fact, I proposed
cyclotomic expansion conjectures and Volume conjectures for superpolynomials.
Another direction for generalization involves the Witten–Reshetikhin–Turaev and(modified) Turaev–Viro quantum invariants of 3-manifolds. In a joint work with
T. Yang, we formulated a new Volume Conjecture for the asymptotics of these 3manifolds invariants evaluated at certain roots of unit, and numerically checked it for
many examples. Interestingly, this conjecture uses roots of unity that are diﬀerent
from the one usually considered in literature. This may indicate that the understanding of this new phenomenon requires new physical and geometric interpretations that
go beyond the usual quantum Chern–Simons theory. I will also introduce a work on
Krillov–Reshetikhin quantum 6j-symbols done by J. Murakami and me.

Inkang Kim KIAS
Title: New way of constructing mapping class group invariant Kähler metrics on
Teichmüller space and the convexity of energy function
Abstract: In this talk, we introduce a new way of constructing Kähler metrics on
Teichmüller space diﬀerent from Weil–Petersson metric. This is done through the energy of harmonic maps. We also give some possible applications for higher Teichmüller
theory. This is a joint work with Wan and Zhang.

11

Taehee Kim Konkuk University
Title: Primary decomposition in knot concordance
Abstract: I will address the conjecture that nonslice knots with coprime Alexanderpolynomials are not concordant. In particular, I will give evidence supporting theconjecture using various concordance invariants. A similar conjecture for smoothknot concordance and Jae Choon Cha’s new framework on the study of primary
decomposition in knot concordance, which includes the above conjecture, will also be
discussed. This is joint work with Min Hoon Kim and Se-Goo Kim.

Takahiro Oba RIMS, Kyoto University
Title: Lefschetz–Bott fibrations and their applications to symplectic geometry
Abstract: A Lefschetz–Bott fibration can be viewed as a complex Morse–Bott function, and, in particular, a Lefschetz fibration is Lefschetz–Bott. As Lefschetz fibrations
have played an important role in symplectic geometry, we expect Lefschetz–Bott fibrations to do that. In this talk, I will first give an overview of some aspects ofLefschetz–Bott fibrations. After this, I will explain their applications to symplectic geometry such as (strong) symplectic fillings of contact manifolds and symplectic
mapping class groups.

Toshie Takata Kyushu University
Title: The strong slope conjecture for cablings and connected sums
Abstract: For a maximal set K of knots which satisfy the Strong Slope Conjectureand some additional conditions, we prove that K is closed under connected sums andcablings. In particular, we establish the Strong Slope Conjecture for graph knots.
This is joint work with Kenneth L. Baker and Kimihiko Motegi.

12

Kokoro Tanaka Tokyo Gakugei University
Title: Independence of Roseman moves for surface knots
Abstract: Roseman moves are seven types of local modifications for (broken surface) diagrams in 3-space which generate ambient isotopies of surface links in 4-space.
Independence of Roseman moves as local moves is already well understood. Then it
is natural to ask what types should appear in any sequence of Roseman moves fortwo diagrams of a given surface knot. In this talk, we discuss independence of Roseman moves involving triple points and also independence of those involving branch
points. The former is a joint work with Kengo Kawamura (Osaka City University)and Kanako Oshiro (Sophia University), and the latter is a joint work with Masamichi
Takase (Seikei University).

13

Parallel Session
Nobutaka Asano Tohoku University
Title: Vertical 3-manifolds in simplified genus 2 trisections of 4-manifolds
Abstract: A trisection is a decomposition of a closed 4-manifold by 3 tuple of 4dimensional 1-handlebodies, which was introduced by Gay and Kirby. They proved
the existence of a trisection for any closed 4-manifold by using a stable map (called atrisection map) from the 4-manifold to R2 . After their work, a simplified trisection was
introduced by Baykur and Saeki. They proved the existence of a simplified trisection
from a simplified broken Lefschetz fibration, by homotopies called Lekili moves. In
this talk, using Lekili moves, we will give a classification of 3-manifolds that can beobtained as the preimages of arcs on R2 by simplified genus 2 trisection maps, which
we call vertical 3-manifolds. The source 4-manifold that admits a given set of vertical
3-manifolds is also determined.

Airi Aso Tokyo Metropolitan University
Title: Twisted Alexander polynomials of tunnel number one Montesinos knots
Abstract: The twisted Alexander polynomial was introduced in 1990’s as a generalization of the Alexander polynomial, which is one of the classical invariants of knots
determined by the fundamental groups of the compliments of knots (i.e., knot groups).
Since the twisted Alexander polynomial of a knot is determined by the knot groupand their representation, it has more information than the classical Alexander polynomial. For example, Kinoshita–Terasaka and Conway’s 11 crossing knots, which are
not distinguished by their Alexander polynomials, are distinguished by their twisted
Alexander polynomials.
The tunnel number of a knot K is the minimal number of mutually disjoint arcs τiin S 3 \ K such that the component of an open regular neighborhood of K ∪ (∪τi ) isa handlebody.
In this talk, we calculate the twisted Alexander polynomials of tunnel number one
Montesinos knots associated to their SL2 (C) representations.

14Benjamin Bode Osaka University
Title: Knotted surfaces as algebraic varieties
Abstract: The loop braid group is the fundamental group of configurations of an
unlink in R3 , where each component lies in a plane parallel to a fixed plane. I will
present an algorithm that constructs for every element B of the loop braid groupa polynomial map f : R5 → R2 such that f −1 (0) ∩ S 4 contains the closure of B.
Moreover, the algorithm provides an upper bound on the degree of the constructed
polynomials. The construction can be generalized to certain elements of other motion
groups. We also highlight applications in theoretical physics, in particular a step towards the construction of electromagnetic fields with closed (and potentially knotted)
field lines, whose time evolution is described by the chosen element of the motion
group.

Jae Choon Cha POSTECH
Title: Primary decomposition in low dimensional topology
Abstract: We introduce the notion of primary decomposition for various abeliangroups which appear in the study of low dimensional topology, and discuss related
conjectures and questions. Key examples include knot concordance groups and rational homology cobordism group of rational homology 3-spheres. For the case of thesmooth concordance group of topologically slice knots, we show that there is a large
subgroup which admits infinitely many primary factors each of which has infinite rank.
This result exhibits the rich structure of the primary decompositions and provides evidences supporting the conjectures. Among the key ingredients of the proof, we use
Cha–Orr’s amenable L2 -signature theorem, Ozsvath–Szabo’s inequality for definite
4-manifolds, and Némethi’s work on Heegaard Floer homology of plumbed manifolds.

Xinghua Gao KIAS
Title: Orderability of Dehn fillings and the L-space conjecture
Abstract: Boyer, Gordon, and Watson conjectured that an irreducible rational
homology 3-sphere is not an L-space if and only if its fundamental group is leftorderable (known as the L-space conjecture). In this talk, I will show how to prove^R) representations.
left-orderability of a fundamental group by constructing P SL(2,15Marı́a de los Angeles Guevara Hernández Osaka City University
Title: The braid alternation number and the braid dealternating number
Abstract: Alexander’s theorem states that any link can be presented as a closed
braid. However, there are alternating links that cannot be presented as an alternatingclosed braid. In this talk, we will introduce the braid alternation number and thebraid dealternating number, which are invariants that measure how far the links arefrom being an alternating closed braid. Furthermore, we will show the value of theseinvariants for some knot families and the gap between their values. This is joint workwith Akio Kawauchi.

Kazuhiro Ichihara Nihon University
Title: Two-bridge knots admit no purely cosmetic surgeries
Abstract: I will talk on cosmetic surgery on knots, i.e., pair of distinct Dehn surgeries
produce 3-manifolds that are homeomorphic as oriented manifolds. Actually it will beshown that two-bridge knots and alternating fibered knots admit no purely cosmetic
surgeries. This talk is based on a joint work with In Dae Jong, Thomas W. Mattman,
and Toshio Saito.

Daiki Iguchi Hiroshima University
Title: The Goeritz groups of bridge decompositions
Abstract: For a bridge decomposition of a link in S 3 , we define the Goeritz group
to be the group of isotopy classes of orientation-preserving diﬀeomorphisms of S 3
that preserve the bridge sphere and link setwise. In this talk, we discuss propertiesof the group, such as the cardinality and the asymptotic behavior of the minimal
pseudo-Anosov entropies. This is a joint work with S. Hirose, E. Kin and Y. Koda.

Ayumu Inoue Tsuda University
Title: The fibered knots whose knot quandles are finite
Abstract: Associated with any dimensional knot, we have its knot quandle in asimilar manner to its knot group. Cardinalities of knot quandles can be finite, while
those of knot groups are always infinite. In this talk, the speaker gives a necessary andsuﬃcient condition for a fibered knot so that its knot quandle is finite. Especially, we
obtain a complete list of classical knots whose twist-spinning have finite knot quandles.

16Katsumi Ishikawa RIMS, Kyoto University
Title: Vanishing of open Jacobi diagrams with odd legs
Abstract: The space of open Jacobi diagrams B is a vector space generated by unitrivalent graphs and plays an important role in quantum topology. In particular, thevanishing of the odd-leg part of B is conjectured and from this conjecture it follows
that the Kontsevich invariant of a knot does not depend on the orientation.
In this talk, we introduce recent results on this conjecture, including the vanishingof the odd-leg part up to loop degree 8.

BoGwang Jeon POSTECH
Title: Rigidity in hyperbolic Dehn fillings
Abstract: In this talk, I will discuss about a rigidity of core geodesics in hyperbolic Dehn fillings. For instance, for a given n-cusped hyperbolic 3-manifold M having non-symmetric cusp shapes, it is shown any Dehn filling of M with suﬃciently
large coeﬃcient is uniquely determined by the product of the holonomies of its coregeodesics.

Gyo Taek Jin KAIST
Title: Minimal grid diagrams of 11 crossing prime alternating knots
Abstract: The arc index of a knot is the length of a minimal arc presentation. An
arc presentation of a knot can be shown in the form of a grid diagram which is a
closed plane curve consisting of finitely many horizontal line segments and the same
number of vertical line segments. The arc index of an alternating knot is its minimal
crossing number plus two. In this talk, we list grid diagrams of the 11 crossing prime
alternating knots obtained from minimal arc presentations which are of length 13. It
is a joint work with Hwa Jeong Lee.

Naoko Kamada Nagoya City University
Title: On almost classical virtual links
Abstract: A virtual link diagram is said to be almost classical if it admits an Alexander numbering. All classical link diagrams are almost classical. In this talk we introduce a map from the set of virtual link diagrams to that of almost classical virtual
link diagrams. It induces a well-defined map from the set of virtual links to that ofalmost classical virtual links.

17

Seiichi Kamada Osaka University
Title: The motion group and the ring group of an H-trivial link and its application
Abstract: An H-trivial link is a link which is equivalent to the split union of someHopf links and a trivial link. We discuss the motion group and the ring group of an
H-trivial link. It turns out that they are isomorphic. A generating set of the group is
given. We also discuss applications to surface knot theory in 4-space. This is a joint
work with C. Damiani and R. Piergallini.

Sungkyung Kang Chinese University of Hong Kong
Title: Link homology theories and ribbon concordances
Abstract: It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard
Floer homology of the branched double cover. I will give a simple proof of a similarstatement in a more general setting, which includes knot Floer homology, Khovanov–Rozansky homologies, and all conic strong Khovanov–Floer theories. I will also discuss
what happens in the case of strongly homotopy ribbon concordances instead of ribbon
concordances.

Hiroaki Karuo RIMS, Kyoto University
Title: On the reduced Dijkgraaf–Witten invariant of knots in the Bloch group of Fp
Abstract: In 2004, Neumann described the hyperbolic volume and the Chern–Simons
invariant of a cusped 3-manifold in terms of the image of the Dijkgraaf–Witten invariant by a certain map. Whereas his work was in C, we describe invariants of thecomplement of a knot by replacing C with a finite field.

Takuya Katayama Hiroshima University
Title: Embeddability between the right-angled Artin groups of surfaces
Abstract: After Kim–Koberda gave a combinatorial description of embeddings between right-angled Artin groups, embeddability of right-angled Artin groups has beenstudied by many researchers. However, very little is known about relation between
the topology of flag complexes and embeddings of right-angled Artin groups. In thistalk, we show the following: for any finite simple graph Λ whose flag complex is
homeomorphic to a 2-sphere, and for any finite simple graph Γ whose flag complex is
homeomorphic to a surface other than a 2-sphere, A(Λ) cannot be embedded in A(Γ).

18Min Hoon Kim POSTECH
Title: Non-slice linear combinations of algebraic knots
Abstract: In 1976, Rudolph asked whether algebraic knots are linearly independent
in the knot concordance group. In this talk, we discuss how to use twisted Blanchfield
pairings to answer this question in the aﬃrmative for new large families of algebraic
knots. This is joint work with Anthony Conway and Wojciech Politarczyk.

Eiko Kin Osaka University
Title: Problem on pseudo-Anosov minimal entropies
Abstract: The aim of this talk is to survey the recent development on the subject.
I will convey why the problem is interesting. I will also explain the significant role offibered faces of hyperbolic fibered 3-manifolds for the study of the problem.

Yuka Kotorii RIKEN
Title: Levine’s classification of 4-component links up to link-homotopy and its classification by claspers
Abstract: Two links are link-homotopic if they are transformed into each other by asequence of self-crossing changes and ambient isotopies. The link-homotopy classes of
4-component links were classified by Levine with enormous algebraic computations.
In this talk, we modify the results by using Habiro’s clasper theory. The new classification gives more symmetrical and schematic points of view to the link-homotopy
classes of 4-component links. We also gives some new subsets of the link-homotopy
classes of 4-component links which are classified by invariants. This is joint work with
Atsuhiko Mizusawa (Waseda University).

Jung Hoon Lee Jeonbuk National University
Title: On Casson–Gordon’s rectangle condition for 3-bridge decompositions of knots
Abstract: For a Heegaard splitting of a 3-manifold, Casson–Gordon’s rectangle condition is a condition on its Heegaard diagram that guarantees the strong irreducibilityof the splitting; it requires 9 types of rectangles for every combination of two pairs ofpants from opposite sides. The rectangle condition is also applied to bridge decompositions of knots. We give examples of 3-bridge decompositions of knots admitting
a diagram with 8 types of rectangles, which are not strongly irreducible, i.e., it saysthat Casson–Gordon’s rectangle condition is sharp. This is a joint work with Bo-hyun
Kwon.

19

Shosaku Matsuzaki Takushoku University
Title: Oriented surfaces in the 3-sphere and their coloring invariants
Abstract: An oriented surface embedded in the 3-sphere S 3 , called a spatial surface,
is presented by a diagram of a trivalent graph in S 3 . Spatial surfaces are characterized
by some local replacements of their diagrams. I will talk on coloring invariants ofspatial surfaces derived from the diagrammatic characterization. This study is joint
work with Atsushi Ishii and Tomo Murao.

Delphine Moussard Aix-Marseille University
Title: Three-dimensional characterization of the slice genus of knots and links
Abstract: A slice knot is a knot in the 3-sphere that bounds a disk smoothly embedded in the 4-ball. More generally, the slice genus of a knot is the minimal genus
of a surface smoothly embedded in the 4-ball and bounded by the knot. We will
prove that the slice genus of a knot can be characterized as the minimal genus of asurface immersed in the 3-sphere except at a finite number of branched points, withno clasp intersection and no triple point of a certain type, and bounded by the knot.
This generalizes a characterization of slice knots by Kawauchi, Shibuya and Suzuki.
Moreover, we will extend this characterization to the slice genus of a colored link.

Tomo Murao University of Tsukuba
Title: Disk systems for handlebody-knots and their isotopy classes
Abstract: A handlebody-knot is a handlebody embedded in the 3-sphere, which canbe regarded as a generalization of a classical knot with respect to a genus. A disk
system of a handlebody-knot is a set of properly embedded non-parallel mutually
disjoint essential disks in the handlebody-knot. In this talk, we discuss the isotopy
classes of pairs of a handlebody-knot and its disk system through discussion on quandle
connected components of multiple conjugation quandles.

20

Takefumi Nosaka Tokyo Institute of Technology
Title: K1 -valued Alexander polynomials of knots
Abstract: The K-groups have provided uniform understanding to several mathematical phenomena. The (twisted) Alexander polynomial is a landmark topic. As its
generalization, we introduce a K1 -class from a group homomorphism from any knot
group to any group. Moreover, we give some approaches to the K1 -class in termsof Reidemeister torsion, Fox derivatives, S 1 -valued Morse theory. As a corollary, wedefined a metabelian Alexander polynomial, and some estimate of fiberedness andsliceness.

Seungsang Oh Korea University
Title: Quantum knot mosaics and bounds of the growth constant
Abstract: The discovery of the Jones polynomial made an important connection
between quantum physics and knot theory. Kauﬀman and Lomonaco introduced theknot mosaic system to define the quantum knot system for the purpose of representing
an actual physical quantum system. This talk is inspired by an open question about
the knot mosaic enumeration suggested by them. A knot m × n-mosaic is an m ×
n array of eleven mosaic tiles representing a knot diagram by adjoining properly.
The total number Dm×n of knot m × n-mosaics, which indicates the dimension of
the Hilbert space of the quantum knot system, is known to grow in a quadratic
exponential rate. Recently, Oh et al. developed the state matrix recursion method
producing the exact enumeration of knot mosaics, which uses a recursion formula ofstate matrices. Furthermore, they showed the existence of the knot mosaic constant1δ = lim (Dm×n ) mn and found its upper and lower bounds in a series of papers.
m,n→∞

The latest upper bound was obtained through two new concepts: quasimosaics andcling mosaics. As a sequel to this research program, we adjust the state matrix
recursion method to handle cling mosaics inside a quasimosaic, which is called theprogressive state matrix recursion method. This method provides recursive matrixrelations producing a sharper bound of the knot mosaic constant:4 ≤ δ ≤ 4.1035507 · · · .

21

Kyungbae Park Seoul National University
Title: On definite fillings of lens spaces
Abstract: The intersection form of a compact, oriented 4-manifold is the intersection
pairing on the second homology group of the manifold. Algebraically, it is a symmetricbilinear form on a finitely generated free abelian group. In this talk, we discuss which
definite forms can be realized as the intersection form of a 4-manifold bounded by agiven lens space. In particular, we completely classify such forms for some familiesof lens spaces. We also present some applications of our classifications. This is joint
work with Dong Heon Choe.

Marco De Renzi Waseda University
Title: 2 + 1-TQFTs from non-semisimple modular categories
Abstract: In recent years, the standard approach of Witten, Reshetikhin, and Turaev
to quantum topology has been substantially generalized thanks to non-semisimple
constructions which have produced powerful 3-manifold invariants and representationsof mapping class groups of surfaces. We will explain how to use the theory of modified
traces in order to renormalize Lyubashenko’s invariants coming from non-semisimple
modular categories. The resulting 3-manifold invariants extend to 2+1-TQFTs, unlike
Lyubashenko’s original ones. Based on a joint work with Azat Gainutdinov, NathanGeer, Bertrand Patureau, and Ingo Runkel.

Shin Satoh Kobe University
Title: The 2-knots of triple point number four
Abstract: The triple point number of a 2-knot is the minimal number of triple points
for all possible diagrams of the 2-knot. It is known that a 2-knot has the triple point
number zero if and only if it is a ribbon 2-knot, and that there is no 2-knot of triple
point number one, two, and three. The aim of this talk is to prove that a 2-knot has
the triple point number four if and only if it is ribbon concordant to the 2-twist-spun
trefoil knot.

22

Donggyun Seo Seoul National University
Title: Dehn twists, right-angled Artin subgroups and trees
Abstract: For an orientable finite type surface, Koberda showed suﬃciently large
powers of Dehn twists and purely pseudo-Anosov mapping classes (on subsurfaces)
generate a right-angled Artin group. In this talk, we will focus on Dehn twists only
and will show that the geometric intersection numbers of the underlying simple closed
curves give a lower bound for exponents of powers to generate a right-angled Artin
group. In the proof, we use tree actions of surface groups.

Kazuto Takao Kyoto University
Title: Local theory of the graphic of two trisections of a 4-manifold
Abstract: The so-called graphic of two Heegaard splittings of a 3-manifold M isvery useful for comparing the splittings. It is the discriminant set of the product map(f, g) : M → R2 of two smooth functions f, g : M → R representing the Heegaard
splittings. By analogy, for comparing two trisections of a 4-manifold X, the discriminant set of the product map (φ, ψ) : X → R4 of two sable maps φ, ψ : X → R2 ishopefully useful. In this talk, I give some local theory on reading oﬀ information fromthe discriminant set, and mention future application of it to global theory.

Hideo Takioka Kyoto University
Title: Vassiliev knot invariants derived from cable Γ-polynomials
Abstract: For coprime integers p (> 0) and q, the (p, q)-cable Γ-polynomial of a knot
K is the Γ-polynomial of the (p, q)-cable knot of K, where the Γ-polynomial is thecommon zeroth coeﬃcient polynomial of the HOMFLYPT and Kauﬀman polynomials.
In this talk, we give some results on Vassiliev knot invariants derived from cable Γpolynomials.

23

Robert Tang OIST
Title: Coarse and fine geometry of the saddle connection graph
Abstract: For a translation surface, the associated saddle connection graph has
saddle connections as vertices, and edges connecting pairs of non-crossing saddle connections. This can be viewed as an induced subgraph of the arc graph of the surface.
In this talk, I will discuss both the fine and coarse geometry of the saddle connection
graph. We prove that the isometry type is rigid: any isomorphism between two suchgraphs is induced by an aﬃne diﬀeomorphism between the underlying translation
surfaces. However, the situation is completely diﬀerent when one considers the quasiisometry type: all saddle connection graphs form a single quasi-isometry class.
Both parts are based on joint work with Valentina Disarlo, Huiping Pan, and Anja
Randecker.

Ryoto Tange Tokyo Denki University
Title: Non-acyclic SL2 -representations of twist knot groups and (−3)-Dehn surgeries
Abstract: We study irreducible SL2 (C)-representations ρ of twist knot groups suchthat the characters tr(ρ) lie on a certain line denoted as x = y. We prove that every
hyperbolic twist knot admits a non-acyclic representation on x = y and that every
ρ on x = y factors through the (−3)-Dehn surgery. This is joint work with Anh T.
Tran and Jun Ueki.

Yuta Taniguchi Osaka City University
Title: Quandle coloring quivers for links and quivers of quandles
Abstract: In 2018, K. Cho and S. Nelson introduced the quandle coloring quiverwhich is an invariant for oriented links. Given a quandle X, a set of quandle endomorphisms S ⊂ End(X) and a link diagram D, the quandle coloring quiver QSX (D)is the directed graph with a vertex for every element in the set of X-colorings of D
and an edge from f to g when g = φ ◦ f for an element φ ∈ S. In this talk, we will
introduce a quiver called the quandle quiver or the quiver of a quandle X, which isa directed graph determined for the pair (X, S) and observe a relation between thequandle coloring quiver of a link and the quandle quiver.

Jun Ueki Tokyo Denki University
Title: Profinite rigidity for twisted Alexander invariants
Abstract: I will discuss the profinite rigidity of twisted Alexander invariants andhyperbolic volumes from a viewpoint of arithmetic topology.
24

Anderson Vera RIMS, Kyoto University
Title: Johnson-type homomorphisms and the Le–Murakami–Ohtsuki invariant
Abstract: One of the main objects associated to a surface Σ is its mapping classgroup M(Σ). By considering the action of M(Σ) on the fundamental group of Σ, it
is possible to define diﬀerent filtrations of M(Σ)together with some homomorphisms
on each term of the filtration, to which we refer as “Johnson-type homomorphisms”.
In this talk we present our results concerning two filtrations of M(Σ), whose definitions involve a handlebody bounded by Σ. We show the relationship between thecorresponding Johnson-type homomorphisms and the functorial extension of the Le–
Murakami–Ohtsuki (LMO) invariant of 3-manifolds.

Hyungkee Yoo Korea University
Title: Small lattice spatial 3-regular graphs with two vertices
Abstract: A lattice spatial graph is an embedding of a graph into the cubic lattice
Z3 . The lattice stick number sL (G) of a spatial graph G is defined to be the minimal
number of straight line segments required to construct a lattice spatial graph. In thistalk, we focus on specific graphs, which are the theta-curve and the handcuﬀ graph.
We rigorously prove that there are exactly six types of spatial graphs with up to 14
lattice sticks corresponding to a theta-curve and a handcuﬀ graph. Their exact lattice
stick numbers are presented.

Seokbeom Yoon KIAS
Title: Adjoint Reidemeister torsions from wrapped M5-branes
Abstract: In this talk, I would like to talk about a certain vanishing property ofadjoint Reidemeister torsions for a hyperbolic 3-manifold which is derived from thephysics of wrapped M5-branes on the manifold. We present a rigorous proof for the
figure-eight knot complement and several numerical experiments. This is joint workwith Dongmin Gang and Seonhwa Kim.

25

Ken’ichi Yoshida Saitama University
Title: Degeneration of 3-dimensional hyperbolic cone structures with decreasing coneanglesAbstract: The global rigidity of a 3-dimensional hyperbolic cone manifold is known
in the case that the cone angles are at most π. The proof of the global rigidity
by Kojima is based on the fact that hyperbolic cone structures do not degenerate in
deformation with decreasing cone angles at most π. In this talk, I will give an example
of degeneration of hyperbolic cone structures with decreasing cone angles less than
2π. These cone structures are constructed on a certain alternating link in T 2 × I.
The construction is reduced to describing dihedral angles for a certain hyperbolic
polyhedron.

Wataru Yuasa RIMS, Kyoto University
Title: The sl3 colored Jones polynomial of a (2, m)-torus link and its tail
Abstract: The sl3 colored Jones polynomial ( sl3 CJP) is one of the quantum invariants of knots and links. I will talk about explicit formulas of sl3 CJP and its limit
called the sl3 tail for a special coloring. In the case of CJP for sl2 , the tail of a (2, m)torus link T (2, m) is described as the Ramanujan’s theta function. I will comment on
the relationship between the sl3 tail of T (2, 2m) and a sl3 theta function.

26

List of Participants
Tetsuya Abe (Ritsumeikan University)

Se-Goo Kim (Kyung Hee University)

Hirotaka Akiyoshi (Osaka City University)

Taehee Kim (Konkuk University)

Nobutaka Asano (Tohoku University)

Naoki Kimura (Waseda University)

Airi Aso (Tokyo Metropolitan University)

Eiko Kin (Osaka University)

Shinpei Baba (Osaka University)

Toshitake Kohno (The University of Tokyo)

Benjamin Bode (Osaka University)

Yuka Kotorii (RIKEN)Jae Choon Cha (POSTECH)

Jung Hoon Lee (Jeonbuk National University)

Qingtao Chen
(New York University Abu Dhabi)

Chaeeun Lim (KAIST)
Yukio Matsumoto (Gakushuin University)

Sangbum Cho (Hanyang University)

Shosaku Matsuzaki (Takushoku University)

Xinghua Gao (KIAS)

Delphine Moussard (Aix-Marseille University)

Hiroshi Goda (Tokyo University ofAgriculture and Technology)

Tomo Murao (University of Tsukuba)
Inasa Nakamura (Kanazawa University)

Kazuo Habiro (RIMS, Kyoto University)

Yasutaka Nakanishi (Kobe University)

Marı́a de los Angeles Guevara Hernández(Osaka City University)
Kazuhiro Ichihara (Nihon University)

Takefumi Nosaka(Tokyo Institute of Technology)

Daiki Iguchi (Hiroshima University)

Takahiro Oba (RIMS, Kyoto University)

Ayumu Inoue (Tsuda University)

Seungsang Oh (Korea University)

Katsumi Ishikawa (RIMS, Kyoto University)

Tomotada Ohtsuki (RIMS, Kyoto University)

Tetsuya Ito (RIMS, Kyoto University)

Kyungbae Park (Seoul National University)

BoGwang Jeon (POSTECH)

Marco De Renzi (Waseda University)

Gyo Taek Jin (KAIST)

Takuya Sakasai (The University of Tokyo)

Naoko Kamada (Nagoya City University)

Shin Satoh (Kobe University)

Seiichi Kamada (Osaka University)

Donggyun Seo (Seoul National University)

Taizo Kanenobu (Osaka City University)

Tatsuro Shimizu (RIMS, Kyoto University)

Sungkyung Kang
(Chinese University of Hong Kong)

Reiko Shinjo (Kokushikan University)

Hiroaki Karuo (RIMS, Kyoto University)
Takuya Katayama (Hiroshima University)

Yuuki Tadokoro (National Institute ofTechnology, Kisarazu College)

Inkang Kim (KIAS)

Akihiro Takano (University of Tokyo)

Min Hoon Kim (POSTECH)

Kazuto Takao (Kyoto University)

Masaaki Suzuki (Meiji University)27

Toshie Takata (Kyushu University)

Jun Ueki (Tokyo Denki University)

Hideo Takioka (Kyoto University)

Anderson Vera (RIMS, Kyoto University)

Baseda Tamotsu (Osaka City University)

Hyungkee Yoo (Korea University)

Kokoro Tanaka (Tokyo Gakugei University)
Seokbeom Yoon (KIAS)

Robert Tang (OIST)Ryoto Tange (Tokyo Denki University)

Ken’ichi Yoshida (Saitama University)

Yuta Taniguchi (Osaka City University)

Wataru Yuasa (RIMS, Kyoto University)28

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29