数理解析研究所講究録 1922

変換群の位相幾何と代数構造

京都大学数理解析研究所
2014 年 10 月

数理解析研究所講究録は，京都大学数理解析研究所の共同利用研究集会および共同研究の記録として 1964 年に刊行が開始されました．現在の共同利用共同研究拠点(2010 年発足) の前身である，全国共同利用研究所として当研究所が発足した翌年のことでしたが，以来半世紀，毎年数十巻を刊行し，2012 年には第 1800 巻が刊行されるに至りました．第 1 巻から第 1840 巻までに収録された論文数は 26,808 編，総頁数は 317,199 頁という膨大なものであり，最先端の数学数理科学分野の研究状況を伝えるのみならず，我が国の数学数理科学の発展の歴史を留める文献として，他に類例を見ない論文集となっています．

講究録の内容は当研究所のウェブサイトおよび京都大学の学術情報リポジトリにおいても公開され，年間の総アクセス数は 1254,383 回 (2012 年度) を数えるなど，多数の方にご利用いただいています．

講究録の使用言語は論文著者の判断に任されていますが，結果的に日本語が多用されていることが特徴の一つとなっています．その結果，講究録は，数学数理科学の広い領域における最先端の専門知識に母国語でアクセスできるものとして，近年の英語化の流れの中で，重要な文献となりつつあります．

当研究所の共同利用事業に参加し講究録の論文を執筆していただいた多数の方々に対し，講究録を大きく成長させていただいたことを深く感謝いたしますとともに，これからも，当研究所の共同利用共同研究拠点としての活動にご参加いただき，講究録の発展にご協力いただけますよう心よりお願い申し上げます．

RIMS$K\hat{o}k\gamma_{1}\hat{/}roku$

1922

The Topology and the Algebraic Structures ofTransformation Groups
May 2630, 2014$\sim$

edited by Takao Satoh$October_{y} 2014$

Research lnstitute for Mathematical Sciences
Kyoto University, Kyoto, Japan
This is a report of research done at the Research Institute for MathematicalSciences, Kyoto University. The papers contained herein are in final form
and will not be submitted for publication elsewhere.

Research Institute for Mathematical Sciences

The Topology and the Algebraic Structures ofTransformation Groups
Organized byTakao Satoh(Tokyo University of Science)

May 26th– May 30th, 2014

Introduction by the Organizer
This is a report on the conference on The Topology and the Algebraic Structuresof Transformation Groups held at the Research Institute for Mathematical Sciences(RIMS), Kyoto University, from May 26 to May 30, 2014.

The theory of transformation groups studies various symmetries of topological spaces,in particular cell complexes and manifolds. One of its origins goes back to Klein’s works
in $1870s$ . It has been developed by a huge number of authors, and has multiple facets
and widespread applications in a broad range of Mathematics, for instance, DiﬀerentialGeometry, Algebraic Geometry, Diﬀerential Topology, Algebraic Topology, Homotopy
Theory, Representation Theory, Group Theory and so on.
A conferece on Ransformation group theory holds at RIMS each year. It has been
going on for forty years since the first conference held in 1973, organized by ProfessorKatsuo Kawakubo. Recent topics discussed in the conference have a great diversity,including the classification of toric manifolds and Bott manifolds, tangential representations and the Simith equivalence, generalizations of the Borsuk-Ulam theorem,
the classification of isovariant maps on smooth manifolds, the structure of definablemanifolds, and the diﬀeomorphism groups and the mapping class groups of surfaces.
Needless to say, these researches have been studied with a wide variety of techniques
including Homology and Homotopy theory, Lie group and Lie algebra theory, -theory
and -theory, Surgery theory, Symplectic geometry and so on. The conferences haveplayed important roles on sharing new developments and new techneques, and on theinteraction of researchers of the field.
$K$

$L$

This conference brought together researchers working in various aspects of the field.
The topics discussed were Transformation group theory in a broad sense. The conferenceof this year was well attended by 54 participants including researchers from abroad,
China, Pohland and Russia. The organizer kept a balance between young researchers(graduate students, post-doctors) and newcomers to the field on the one hand, andsenior specialists on the other hand. We hope that this report goes a long way toward

providing valuable images of further developments of the field.
The organizer would like to express his sincere gratitude to all participants for his/her
contribution to the success of the conference. He also thanks to all secretaries working atRIMS, in particular Ms. Sachiko Murayama for her continued supports for site management and accounting works, and Ms. Yuko Watanabe for editing this report. Finally,the organizer expresses his sincere appreciation to RIMS for the financial support andits warm hospitality.
Takao Satoh
Kagurazaka, Tokyo
September 2014

-equivariant cohomology rings of Springer varietieLg (Joint work with Hiraku Abe)$\sim$

16:50 Fumihiro Ushitaki (Kyoto Sangyo University)$\sim$

10:50 Tatsuhiko Yagasaki (Kyoto Institute of Technology)

14:00 14:50 Miho Hatanaka (Osaka City Umversity)
Spin toric manifolds constructed from graphs

14:55 15:45 Masayuki Kawashima (Tokyo University of Science)$\sim$

10:50 Hiroaki Ishida (RIMS)$\sim$

11:00 11:50 Hisashi Kasuya (TITech)
An extension of the Nomizu, Hattori and Mostow theoremsInfinitesimal automorphisms on moment-angle manifolds with complex-analytic structures

10:00

27th May 2014$\sim$

15:50 16:50 Kohhei Yamaguchi (University of ElectroCommumcations)
The space of maps to a real toric varietv

rangements

On Alexander polynomials andCharacteristic Varieties of Namba-Tsuchihashi ar-$\sim$$\sim$

Please turn over.

16:00 16:50 Yoshimi Shitanda (Meiji University)
The degree of set-valued mappings from ANR spaces to homology spheres$\sim$

15:00 15:50 Yusuke Suyama (Osaka City University)
Examples of toric manifolds whose orbit spaces by the compact torus are not simple
polytopes$\sim$$\sim$

13:00 13:50 Naoyuki Monden (Osaka ElectrGCommunication University)
Letschetz $penci1_{bd}nd$ huutely presented groups (Joint work with Ryoma Kobayashi)$\sim$

Young diagraans and intersection numbers for toric manifolds arising from root systems$\sim$$\sim$

11:00 11:50 Hiraku Abe (OCAMI)-cones and deformation of uniform embeddings$\kappa$

10:00

28th May 2014

Borsuk-Ulam type theorems and Isovariant maps (Joint work with Ikumtsu Nagasaki)

16:00

15:00 15:50 Haozhi Zeng (Osaka City University)
The cohomology of toric origami manifolds$T^{\iota}$$\sim$

The$\sim$

14:00 14:50 Tatsuya Horiguchi (Osaka City University)

14:00 14:50 Takeshi Harui (Kogakuin University)
Automorphism groups and plane models of Riemann surfaces$0-$$\sim$

13:00 13:50 Yasuhiro Hara (Osaka University)
On the topology of simphcial complexes associated with graphs

10th Aipril 2014 version

13:00 13:50 Tomohiro Kawakami (Wakayama University)
Definable slices in -minimal structures

Program

Kitashirakawaoiwake-cho, Sakyo, Kyoto citv, 606-8502, Japan

26th May 2014

Address:

Date: May 26–30, 2014
Place: Research Institute for Mathematical Science in Kyoto Universitv

email: takao@rs.tus.ac jp

Organizer: Satoh, Takao (Tokyo University of Science)matical Science in Kyoto University.

We are planning to hold the conference supported by Research Institute for Mathe-The Topology and the Algebraic Structures ofTransformation Groups

RIMS Conference

$t\succ$$\sim$

11:00 11:50 Toshiyuki Akita (Hokkaido University)
primary components of the homology of Coxeter groups$\sim$

10:00 10:50 Mitsunobu Tsutaya (Kyoto University)
On evaluation fiber sequences

30th May 2014$\sim$

15:55 16:55 Masaharu Morimoto (Okayama University)
Tentative study on equivariant surgery obstractions$\sim$

14:50 15:50 Krzysztof Pawalowski (Adam Mickiewicz University)
Group actions on homotopy complex projective spaces$\sim$

13:55 14:45 Shintaro Kuroki (The University of Tokyo)
On complexlty one GKM graphs wlth symmetries$\sim$

13:00 13:50 Daisuke Kishimoto (Kyoto University)
Homotopy decomposition of diagonal arrangements$\sim$

11:00 11:50 Tsuji Shunsuke (The University of Tokyo)
The logarithms of Dehn twists on unorientable surfaces$\sim$

10:00 10:50 Anton Ayzenberg (Osaka City University)
Quasitoric manifolds which are not toric ongami manifolds

29th May 2014

変換群の位相幾何と代数構造

The Topology and the Algebraic Structures of Transformation Groups
RIMS 研究集会報告集
2014 年 5 月 26 日 $\sim 5$ 月 30 日
研究代表者

佐藤隆夫 (Takao Satoh)次目

1. Definable slices in -minimal structures

1$0$

和歌山大・教育 (Wakayama U.)

川上智博 (Tomohiro Kawakami)

2. On automorphism grouPs and plane models of Riemann surfaceS
工学院大学習支援センター (Kogakuin U.) 春井 岳 (Takeshi Harui)

8

3. On Alexander polynomials of some reduced curves

21

東京理大理 (Tokyo U. Sci.)

川島正行 (Masayuki Kawashima)

4. Spaces of equivariant maps to toric varieties
電通大情報理工学 (UEC)山口

5. Nomizu, Hattori, Mostow の定理の発展

糟谷久矢 (Hisashi Kasuya)

グラフから定まる単体複体の位相について
阪大理学 (Osaka U.)38
原靖浩 (Yasuhiro Hara)

洲本実業高校 (Sumoto Ind. Senior High Sch.) 冨田

7. シュプリンガー多様体の8.

耕平 (Kohhei Yamaguchi)–34

東工大理工学 (Tokyo Inst. Tech.)6.

28$T^{\mathfrak{g}}$優次 (Yuji Tomita)-同変コホモロジー環

50

大阪市大数学研 (Osaka City U.)

阿部拓 (Hiraku Abe)

大阪市大理学 (Osaka City U.)

堀口達也 (Tatsuya Horiguchi)

Cohomology of toric origami manifolds55

大阪市大理学 (Osaka City U.)

Haozhi Zeng

9. On G-bi-isovariant equivalence between -representation spaces
60
京都府立医大 (Kyoto Pref. U. Medicine)
長崎 生光 (Ikumitsu Nagasaki)$G$

京産大理 (Kyoto Sangyo U.)

牛瀧

$i$

文宏 (Fumihiro Ushitaki)

10. Local and end deformation properties of uniform embeddings in -cones65$\kappa$

京都工繊大工芸科学 (Kyoto Inst. Tech.)矢ケ崎

達彦 (Tatsuhiko Yagasaki)

1 1. ルート系から定まるトーリック多様体上の交叉数とヤング図
阿部 拓 (Hiraku Abe)
大阪市大数学研 (Osaka City U.)

78

12. Lefschetz pencil and finitely presented groups84

東京理大理工 (Tokyo U. Sci.)

小林竜馬 (Ryoma Kobayashi)

大阪電通大 (Osaka Electro-Communi. U.)

門田直之 (Naoyuki Monden)

13. グラフから構成されるスピントーリック多様体

90
畑中

大阪市大理学 (Osaka City U.)

美帆 (Miho Hatanaka)

14. コンパクトトーラスによる軌道空間が単純な多面体でない toric manifold の例 96
須山 雄介 (Yusuke Suyama)
大阪市大理学 (Osaka City U.)
1 5. ANR 空間からホモロジー球面への集合値写像の次数
四反田

明治大政治経済 (Meiji U.)

16. Quasitoric manifolds which are not toric origami
大阪市大理学 (Osaka City U.)

義美 (Yoshimi Shitanda)

112
Anton Ayzenberg枡田’$\prime$102

幹也 (Mikiya Masuda)

Seonjeong ParkHaozhi Zeng

Nat. lnst. Math. Sci.
大阪市大理学 (Osaka City U.)

17. 非有向曲面におけるデーン・ツイスト、 ゴールドマンリー代数と124

スケイン加群辻俊輔 (Shunsuke Tsuji)

東大数理科学 (U. Tokyo)

18. 対角部分空間配置のホモトピー分解130
岸本

京大理学 (Kyoto U.)

大祐 (Daisuke Kishimoto)

19. Classifications of homogeneous complexity one GKM manifolds and GKM graphswith symmetric grouP actions
黒木

東大・数理科学 (U. Tokyo)

135

慎太郎 (Shintar\^o Kuroki)

2 O. Group actions on complex projective spaces via group actions on disks and spheres– 147
Marek Kaluba
Adam Mickiewicz U.
’/Krzysztof Pawalowskiii21. Tentative study on equivariant surgery obstructions:Fixed point sets of smooth$A_{5}$-actions154

岡山大・自然科学 (Okayama U.)

森本

雅治 (Masaharu Morimoto)

22. On evaluation fiber sequences

166

京大理学 (Kyoto U.)

23. Coxeter 群のホモロジーの

蔦谷

$P$

充伸 (Mitsunobu Tsutaya)-primary component について

北大理学 (Hokkaido U.)

秋田

$m$

利之 (Toshiyuki Akita)170