• 日程・場所

2023 年 9 月 4 日 (月) – 9 月 7 日 (木) 中央大学理工学部，５号館 1 階５1３４号室

112-8551 東京都文京区春日 1-13-27• 講演予定者

Elmar Vogt (Freie U., Berlin), Gaë l Meigniez (U. Aix-Marseille), Sam Nariman (Purdue U.),
坪 井 俊 （ 武 蔵 野 大 学 ）， 森 田 茂 之 （ 東 京 大 学 ）， 森 吉 仁 志 （ 名 古 屋 大 学 ）， 三 松 佳 彦 (中 央 大 学)，
北野晃朗（創価大学）

Filip Samuelsen（Stony Brook U.), Shuhei Maruyama (Chuo U.), KyeongRo Kim (Seoul National U.)• Date and Venue

September 4th (Mon.) – September 7th (Thur.), 2023
Room: 5134, Ground �loor, No. 5 Building,

Faculty of Science and Engineering, Chuo University, 1-13-27
Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan• Speakers

Elmar Vogt (Freie U., Berlin), Gaë l Meigniez (U. Aix-Marseille), Sam Nariman (Purdue U.),
Takashi Tsuboi (Musashino U.), Shigeyuki Morita (U. Tokyo), Hitoshi Moriyoshi (Nagoya U.),
Yoshihiko Mitsumatsu (Chuo U.), Teruaki Kitano (Soka U.)

Filip Samuelsen（Stony Brook U.), Shuhei Maruyama (Chuo U.), KyeongRo Kim (Seoul National U.)

1• Time Schedule:
9/4 (Mon)
11:00-12:20 Gaë l Meigniez -1
14:00-15:20 Takashi Tsuboi
15:50-17:10 Elmar Vogt -1

9/5 (Tues)
10:00-11:20 Teruaki Kitano
11:40-12:40 Shigeyuki Morita
14:30-15:30 Short communications 1, 2, 3
9/6 (Wed)
10:00-11:00 Elmar Vogt -2
11:20-12:20 Yoshihiko Mitsumatsu -1
14:00-15:20 Gaë l Meigniez -2
15:50-17:10 Sam Nariman -1

9/7 (Thur)
10:00-11:00 Yoshihiko Mitsumatsu -2
11:20-12:20 Hitoshi Moriyoshi
14:00-15:20 Sam Nariman -2
15:50-17:10 Gaë l Meigniez -3
17:30 Banquet• Title and Abstract

1.

Gaë l Meigniez (Université de Aix-Marseille):BΓ basics

Abstract: this will be an elementary, introductory microcourse on the classical homotopy theoryof foliations:
Bott's obstructions, Godbillon-Vey, BΓ, the h-principle for foliations, the Mather-Thurston theory,and the Hae�liger-Thurston conjecture.
2. Homotopy types of foliations spaces by surfaces

Abstract: It will be shown that on every closed manifold of dimension at least 4, the space of the smooth
foliations of dimension 2 has the same weak homotopy type as the space of the distributions of 2-planes.
Takashi Tsuboi (Musashino University / RIKEN iTHEMS):

B𝛤𝛤� 𝜔𝜔 and 𝐻𝐻1 (Diff 𝜔𝜔 (𝑀𝑀)0 ) for M with circle action

Abstract: In the �irst part of my talk, we review some of the works of André Hae�liger on the classifying
spaces for real-analytic 𝛤𝛤�-structures. The current situation looks almost the same as at the time whenHae�liger treated them.
In the second part, we explain that the identity component of the group of real-analytic
diffeomorphisms of a closed manifold is perfect if the manifold admits a semi-free circle action. This
follows from that there is a non-trivial equivariant map from manifolds with semi-free circle action tothe complex line.

2Elmar Vogt (Freie Universitä t Berlin, Emeritus):

The Mather-Thurston Theorem: Mather’s 1976 write-up of Thurston’s third proof. An Overview

Abstract: We begin with a brief introduction to Hae�liger structures and their relationship to foliations
and their homotopy (concordance) classi�ication. Roughly the Mather-Thurston theorem relates thegroup of diffeomorphism with compact support of an n-manifold M with the space of compactly
supported sections of a �ibration over M with �ibre the classifying space of Hae�liger structures ofcodimension n with trivialized normal bundle.
The proof of Mather is based on talks given by Thurston and is quite involved. We will outline the key
steps and describe the many spaces and maps between them which �igure in the proof.
Teruaki Kitano (Soka University):

Remarks on �lat 𝑆𝑆 1 -bundles, 𝐶𝐶 ∞ vs 𝐶𝐶 𝜔𝜔Abstract: We describe low dimensional homology groups of the real analytic, orientation preserving
diffeomorphism group of 𝑆𝑆 1 in terms of B𝛤𝛤�1 by applying a theorem of Thurston. It is an open problem
whether some power of the rational Euler class vanishes for real analytic �lat 𝑆𝑆 1 -bundles. In this talk wediscuss that if it occurs, then the homology group should contain many torsion classes which vanish in
the smooth case. This talk is based on a joint work with Shigeyuki Morita and Yoshihiko Mitsumatsu.

Shigeyuki Morita (University of Tokyo, Emeritus):

Questions on 𝐵𝐵𝛤𝛤�1Abstract: We discuss a few questions about the homotopy type and the homology group of Hae�liger’sclassifying space for foliations of codimension one. We consider differences between consequences of
two extremal models for it, one is the Eilenberg-MacLane space K(R,3) and the other is the Moore space
M(R,3). This talk is based on joint work with Teruaki Kitano and Yoshihiko Mitsumatsu.
Yoshihiko Mitsumatsu (Chuo University):

Mather-Thurston maps for the �lat real analytic circle bundles

Abstract: Under the real analytic setting, there is no reason for the Mather-Thurston map to induce
isomorphism on the homology. In the case of codimension 1, and for �lat circle bundles, we show that adifference from and a similarity to being isomorphic in homology or in homotopy of the MatherThurston map. One of the key ingredient is a �ine analysis on the 1-dimensional real analytic diffeo germs
by 1-dimensional holomorphic dynamics, namely the theory of parabolic linearization. This is based ona joint work with Shigeyuki Morita and Teruaki Kitano.

3Sam Nariman (Purdue University):1.

Some applications of Mather-Thurston's theorem

2.

Bounded and unbounded cohomology of diffeomorphism groupsHitoshi Moriyoshi (Nagoya University):

Abstract: I will talk about two applications of the Mather-Thurston theorem. The �irst one is about PL
homeomorphisms of surfaces. We discuss that Greenberg's work on PL foliations can be used to prove
the Hae�liger-Thurston conjecture for codimension 2 PL foliations and as a result, we could answer thecase of surfaces of a question posed by Epstein in 1970 about the simplicity of PL homeomorphisms thatare isotopic to the identity. If time permits, I will talk about another application of using the MatherThurston theorem in an equivariant setting. And I will answer a question posed by Hae�liger about thepowers of the Euler class for �lat odd-dimensional sphere bundles.

Abstract: Bounded cohomology for groups and spaces was originally de�ined by Gromov in the 80s and it
is intimately related to the geometric and dynamical properties of the groups. For example, Ghys used
the bounded Euler class to classify certain group actions on the circle up to (semi)conjugacy. However,unlike group cohomology, it is notoriously dif�icult to calculate the bounded cohomology of groups. Andin fact, there is no countably generated group known for which we can completely calculate the bounded
cohomology unless it is trivial in all positive degrees like the case of amenable groups. In this talk, I willtalk about joint work with Nicolas Monod on the bounded cohomology of certain homeomorphisms anddiffeomorphism groups. In particular, we show that the bounded cohomology of Diff(𝑆𝑆 1 ) and Diff(𝐷𝐷2 )are polynomial rings generated by the Euler class.
If time permits, I also discuss our solution to Ghys' question about generalizing Milnor-Wood inequality
to �lat 𝑆𝑆 3 -bundles. In particular, we show that the Euler class for �lat 𝑆𝑆 3 -bundles is an unbounded class.

Geometry on the circle diffeomorphism group and the space of equicentroaf�ine curves

Abstract: A plane curve 𝛾𝛾: 𝑆𝑆 1 → 𝑹𝑹2 is called equi-centro-af�ine if the position vector 𝛾𝛾 and the velocity
vector γ ' makes a triangle of constant area with respect to the origin. In other words, the determinant of
2 by 2 matrix (𝛾𝛾 𝛾𝛾 ') is constant. Even though the space M of all equicentroaf�ine curves is in�inite
dimensional, M admits a transitive action by the circle diffeomorphism group due to Pinkall. It is also
known that there exists an invariant pre-symplectic form on M, called the Fujioka-Kurose 2-form. In thistalk we shall manifest an intriguing interaction between Geometry and Analysis, namely a beautiful
relationship among curvature of equicentroaf�ine curves, moment map, the Bott-Virasoro group and theKdV equation. This is a joint work with A. Fujioka and T. Kurose.

Short Communications:Filip Samuelsen（Stony Brook U.) Complex structures on open manifolds

Abstract: On open almost complex manifolds, Hae�liger's framework reduces the problem of constructing
complex structures to a homotopy lifting problem. This short communication presents Masahisa Adachi'stheorem, which asserts that the relevant homotopy �iber is at least n-connected. As a notable corollary, weestablish that any open almost complex manifold with a real dimension of at most 6 admits a complex
structure.

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Shuhei Maruyama (Chuo U.) On the boundedness of characteristic classes for foliated symplectic andcontact �ibrations

Abstract: In this talk, we will discuss the relationship between the boundedness of characteristic classes
for foliated bundles and the descendibility of quasimorphisms. We will also present two speci�iccharacteristic classes for foliated symplectic and contact �ibrations: one is a bounded class, and the otheris an unbounded class.
KyeongRo Kim (Seoul National U.) Invitation to laminar group theory

Abstract : Thurston tried to combine the study of geometric structures and the study of tautly foliated 3–
manifolds to solve the geometrization conjecture. He �irst observed that the fundamental group of a three
manifold admitting a R-covered uniform taut foliation acts on the circle preserving a pair of circle
laminations. In this talk, I brie�ly introduce some notions related to circle laminations and I explain theinteraction between the dynamics on the circle and the topology of hyperbolic manifolds via circle
laminations.
• Access

About a 15-minute walk from JR Soubu Line Suidoubashi Station

About a 5-minute walk from Tokyo Metro Marunouchi Line or Nanboku Line Kourakuen Station

About a 7-minute walk from Tokyo Metro Mita Line or O-edo Line Kasuga Station
Click here for a map (in Japanese)

Organizers:

Click here for a map (in English)

Yoshihiko Mitsumatsu (Chuo Univ.), Teruaki Kitano (Soka Univ.)
E-mail: yoshi(-AT-)math.chuo-u.ac.jp, kitano(-AT-)soka.ac.jp

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