Program
17 September Tuesday
Place : West Bldg.8W, Ookayama Campus, Tokyo Institute of Technology
Room: W1008
15:00-16:00 Tetsuya Abe
The construction of smoothly slice knots 1
We review the construction of Cappell-Shaneson’s (homotopy) 4-spheres
and Gompf’s 4-spheres. Then we explain how to obtain (possibly non-ribbon)
slice knots from these 4-spheres.

18 September Wednesday
Place : West Bldg.8W, Ookayama Campus, Tokyo Institute of Technology
Room: W809
9:30-10:30 Tetsuya Abe
The construction of smoothly slice knots 2
We review the construction of (possibly non-ribbon) slice knots via annulus
twists. We also explain some suﬃcient conditions for given slice knots to beribbon. (arXiv:1305.7492v2)
11:00-12:00 Hye Jin Jang
Introduction to (h)-solvable ﬁltration on the knot concordancegroup
We review the deﬁnition of the (h)-solvable ﬁltration on the knot concordance group deﬁned by Cochran, Orr, and Teichner. We discuss the development of obstructions for detecting (h)-solvability of knots, and known results
about (h)-solvable ﬁltration. Finally, we provide new 2-torsion elements inthe knot concordance group related to this ﬁltration.

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13:00-14:00 Motoo Tange
Knot concordance invariants coming from Floer homology
We review some knot concordance invariants τ (K), δ(K), and dS−1 (K),originated by Heegaard Floer homology. We discuss the relations of thoseinvariants and the computation.
14:30-15:30 Min Hoon Kim
Introduction to bipolar ﬁltration
We review the deﬁnition of the bipolar ﬁltration of topologically slice knots
and survey the recent results of Cochran-Harvey-Horn, Cochran-Horn andCha-Powell. Also, we discuss open problems.

19 September Thursday
Place : West Bldg.8W, Ookayama Campus, Tokyo Institute of Technology
Room: W1008
9:30-10:30 Min Kyoung SongIntroduction to Conant-Schneiderman-Teichner’s ﬁltrations on(string) links
We review the Whitney tower ﬁltration of order on the set of concordanceclasses of (string) links. The ﬁltrations are completely classiﬁed by Milnor
invariants together with new higher-order Sato-Levine invariants and higherorder Arf invariants. Additionally, we see the relationship with Johnson
ﬁltrations and Goussarov-Habiro Y-ﬁltrations on the group of concordanceclasses of string links and the group of homology cobordism classes of homology cylinders.
11:00-12:00 Hye Jin Jang
Kauﬀman conjecture
In 1982, Kauﬀman conjectured that sliceness of a knot K can be readoﬀ from the information of curves on any Seifert surfaces of K. Recently,
Cochran and Davis proved that the Kauﬀman conjecture is false for knots.
(arXiv:1303.4418) We prove that the link version Kauﬀman conjecture is also
false. This is a joint work with Minhoon Kim and Mark Powell.
213:00-14:00 Min Hoon Kim
Whitney towers, grope and Casson-Gordon style invariants oflinks
S. Friedl and M. Powell introduced a Casson-Gordon style invariant for 2component links with linking number 1. Motivated from the seminal work of
Cochran-Orr-Teichner, they conjectured that their invariant is an obstruction
to being height 3.5 Whitney tower/grope concordant to the Hopf link. We
give a proof of this conjecture. If time allows, we give generalizations of theclassical results of J. Hillman and A. Kawauchi.
14:30-15:30 Min Kyoung SongThe homology cobordism group of homology cylinders with newhomomorphism invariants
The homology cobordism group of homology cylinders is enlargement ofboth the mapping class group and the concordance group of string links
in homology D2 × I. We see the structure of the group via the ﬁltrationof extended Milnor invariants. We also obtain Hirzebruch-type intersection
form defect invariants, which can detect inﬁnitely many elements invisible byexisting homomorphism invariants.

20 September Friday
Place : Main Bldg, Ookayama Campus, Tokyo Institute of Technology
Room: H206
10:00-11:00 Tetsuya AbeIntroduction to Rasmussen’s s-invariant
We brieﬂy review Rasmussen’s s-invariant for knots.
11:20-12:00 Keiji Tagami
Rasmussen invariants of almost positive knots
It is known that the Rasmussen invariants of positive knots are computedfrom their positive diagrams. We compute the Rasmussen invariants of almost positive knots from almost positive diagrams.
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