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2012 Fiscal Year Final Research Report

Groups of diffeomorphisms of manifolds

Research Project

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Project/Area Number 20244003
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

TSUBOI Takashi  東京大学, 大学院・数理科学研究科, 教授 (40114566)

Co-Investigator(Kenkyū-buntansha) ASUKE Taro  東京大学, 大学院・数理科学研究科, 准教授 (30294515)
KAWAZUMI Nariya  東京大学, 大学院・数理科学研究科, 准教授 (30214646)
HAYASHI Shuhei  東京大学, 大学院・数理科学研究科, 准教授 (20247208)
KANAI Masahiko  東京大学, 大学院・数理科学研究科, 教授 (70183035)
Co-Investigator(Renkei-kenkyūsha) ASAOKA Masayuki  京都大学, 大学院・理学研究科, 准教授 (10314832)
OHSHIKA Kenichi  大阪大学, 大学院・理学研究科, 教授 (70183225)
NAKAYAMA Hiromichi  青山学院大学, 理工学部, 教授 (30227970)
NODA Takeo  東邦大学, 理学部大阪大学, 准教授 (90431618)
FUJIWARA Koji  東北大学, 大学院・情報科学研究科, 教授 (60229078)
MINAKAWA Hiroyuki  山形大学, 地域教育文化学部, 准教授 (30241300)
MORIYOSHI Hitoshi  慶應義塾大学, 理工学部, 准教授 (00239708)
Project Period (FY) 2008 – 2012
Keywords幾何学 / トポロジー / 多様体 / 微分同相群 / 分類空間 / 力学系 / 離散部分群 / 位相亜群 / 葉層構造
Research Abstract

We studied the group of diffeomorphisms which is the automorphism group of the manifold structure. The principal investigator obtained results on the perfectness of the identity component of the group of real-analytic diffeomorphisms,the uniform perfectness and the uniform simplicity of the identity component of the group of smooth diffeomorphisms, and published them. The co-investigators obtained results on the mapping class group of surfaces, on the transversely holomorphic foliations, on connecting lemma in the theory of dynamical systems, and published them. Each year we organized meeting on the diffeomorphism groups for the collaboration and exchange the research ideas.

  • Research Products

    (41 results)

All 2012 2011 2010 2009 2008

All Journal Article (18 results) (of which Peer Reviewed: 16 results) Presentation (22 results) Book (1 results)

  • [Journal Article] On the uniform perfectness of the groups of diffeomorphisms ofeven-dimensional manifolds2012

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      CommentariiMathematici Helvetici

      Volume: 87 Pages: 141-185

    • DOI

      DOI:10.4171/CMH/251.

    • Peer Reviewed
  • [Journal Article] On Fatou-Julia decompositions of pseudosemigroups II2011

    • Author(s)
      T. Asuke
    • Journal Title

      RIMS Kokyuroku, Research on Complex Dynamics and Related Fields

      Volume: 1762 Pages: 125-133

  • [Journal Article] Applications of Mane's C^2 Connecting Lemma2010

    • Author(s)
      S. Hayashi
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 138 Pages: 1371-1385

    • Peer Reviewed
  • [Journal Article] A Fatou-Julia decomposition of transversally holomorphic Foliations2010

    • Author(s)
      Taro Asuke
    • Journal Title

      Ann. Inst. Fourier (Grenoble)

      Volume: 60 Pages: 1057-1104

    • Peer Reviewed
  • [Journal Article] Godbillon-Vey class of transversely holomorphic foliations2010

    • Author(s)
      Taro Asuke
    • Journal Title

      MSJ memoirs

      Volume: 24 Pages: 1-130

    • Peer Reviewed
  • [Journal Article] On Fatou-Julia decompositions of pseudosemigroups2010

    • Author(s)
      Taro Asuke
    • Journal Title

      数理解析研究所講究録

      Volume: 1699 Pages: 137-143

  • [Journal Article] Classifying spaces for groupoid structures2009

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Contemporary Mathematics

      Volume: 498 Pages: 67-81

    • Peer Reviewed
  • [Journal Article] On the group of real analytic diffeomorphisms2009

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Annales Scientifiques de l'Ecole Normale Superieure

      Volume: 49 Pages: 601-651

    • Peer Reviewed
  • [Journal Article] On the uniform simplicity of diffeomorphism groups2009

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Proceedings of the VIII International Colloquium

      Pages: 43-55

    • Peer Reviewed
  • [Journal Article] On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one2009

    • Author(s)
      Taro Asuke
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 56 Pages: 39-47

    • Peer Reviewed
  • [Journal Article] On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one2009

    • Author(s)
      Taro Asuke
    • Journal Title

      Proceedings of the VIIInternational Colloquium

      Pages: 65-74

    • Peer Reviewed
  • [Journal Article] Infinitesimal derivative of the Bott class and the Schwarzian derivatives2009

    • Author(s)
      Taro Asuke
    • Journal Title

      Tohoku Math. J.

      Volume: 61 Pages: 393-416

    • Peer Reviewed
  • [Journal Article] Codimension one minimal foliations and the fundamentalgroups of leaves2008

    • Author(s)
      T.Yokoyama and T. Tsuboi
    • Journal Title

      Annale de l'InstitutFourier

      Volume: 58 Pages: 723-731

    • Peer Reviewed
  • [Journal Article] On the simplicity of the group of contactomorphisms2008

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: 52 Pages: 491-504

    • Peer Reviewed
  • [Journal Article] On the uniform perfectness of diffeomorphism groups2008

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: 52 Pages: 505-524

    • Peer Reviewed
  • [Journal Article] Twisted Morita-Mumford classes on braid groups2008

    • Author(s)
      N. Kawazumi
    • Journal Title

      Geometry and Topology Monograph series

      Volume: 13 Pages: 293-306

    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

    • Author(s)
      T. Akita and N. Kawazumi
    • Journal Title

      Math. Proc. Camb. Phil. Soc.

      Volume: 144 Pages: 411-421

    • Peer Reviewed
  • [Journal Article] On the stable cohomology algebra of extended mapping class groups for surfaces2008

    • Author(s)
      N. Kawazumi
    • Journal Title

      Advanced Studies in Pure Math.

      Volume: 52 Pages: 383-400

    • Peer Reviewed
  • [Presentation] 剛的な複素二次特性類の非自明性と独立性について2012

    • Author(s)
      足助太郎
    • Organizer
      2011年度複素力学系研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-01-26
  • [Presentation] A C^2 generic trichotomy for diffeomorphisms2011

    • Author(s)
      林修平
    • Organizer
      力学系研究集会
    • Place of Presentation
      東京工業大学
    • Year and Date
      20110100
  • [Presentation] A geometric approach to the higher Johnson homomorphisms2011

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「離散群と双曲空間の解析と幾何」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-12-13
  • [Presentation] On the creation of observable periodic orbits for diffeomorphisms2011

    • Author(s)
      Shuhei Hayashi
    • Organizer
      RIMS研究集会「力学系とトポロジーのフロンティア」
    • Place of Presentation
      京都大学
    • Year and Date
      2011-11-24
  • [Presentation] On the $C^1$-creation of good periodic orbits2011

    • Author(s)
      Shuhei Hayashi
    • Organizer
      Geometry and Dynamics, Todai Forum
    • Place of Presentation
      Ecole Normale Superieure de Lyon (France)
    • Year and Date
      2011-10-18
  • [Presentation] Homeomorphism groups of commutator width one,2011

    • Author(s)
      Takashi Tsuboi
    • Organizer
      Geometry and Dynamics,Todai Forum
    • Place of Presentation
      Ecole Normale Superieure de Lyon (France)
    • Year and Date
      2011-10-17
  • [Presentation] its relatives and rigidity2011

    • Author(s)
      Masahiko Kanai, Cross ratio
    • Organizer
      Geometry and Dynamics, Todai Forum
    • Place of Presentation
      Ecole Normale Superieure de Lyon (France)
    • Year and Date
      2011-10-17
  • [Presentation] Infinitesimal deformations of foliations and Cartan connections2011

    • Author(s)
      Taro Asuke
    • Organizer
      Geometry and Dynamics, Todai Forum
    • Place of Presentation
      Ecole Normale Superieure de Lyon (France)
    • Year and Date
      2011-10-17
  • [Presentation] A $C^2$ generic obstruction to hyperbolicity for diffeomorphisms with dominated splittings2011

    • Author(s)
      Shuhei Hayashi
    • Organizer
      Beyond Uniform Hyperbolicity 2011
    • Place of Presentation
      Marseille, France
    • Year and Date
      2011-06-08
  • [Presentation] On the Turaev cobracket on the Lie algebra of symplectic derivations2011

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM
    • Place of Presentation
      University of Aarhus
    • Year and Date
      2011-01-26
  • [Presentation] The Chas-Sullivan conjecture for a surface of infinite genus2010

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「トポロジーの現在と未来」
    • Place of Presentation
      文部科学省共済組合箱根宿泊所
    • Year and Date
      2010-12-21
  • [Presentation] On Fatou-Julia decompositions2010

    • Author(s)
      足助太郎
    • Organizer
      2010年度複素力学系研究集会--複素力学系とその周辺分野の研究--
    • Place of Presentation
      京都大学
    • Year and Date
      2010-12-09
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Workshop 'Teichmueller Theory'
    • Place of Presentation
      MathematischesForschungsinstitut Oberwolfach
    • Year and Date
      2010-12-03
  • [Presentation] A Fatou-Julia decomposition for transversely holomorphic foliations2010

    • Author(s)
      足助太郎
    • Organizer
      第53回函数論シンポジウム
    • Place of Presentation
      名城大学サテライト
    • Year and Date
      2010-11-22
  • [Presentation] The Goldman Lie algebra and Kontsevich's associative symplectic geometry2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM
    • Place of Presentation
      University of Aarhus
    • Year and Date
      2010-09-28
  • [Presentation] On the uniform perfectness of the group of diffeomorphisms2010

    • Author(s)
      Takashi Tsuboi
    • Organizer
      Conference on Geometry and Topology of Foliations
    • Place of Presentation
      Centro de Recerca Matematica, Barcelona
    • Year and Date
      2010-07-13
  • [Presentation] ${Diff}^¥omega(CP^2)_0$2009

    • Author(s)
      坪井俊
    • Organizer
      「複素解析的ベクトル場・葉層構造とその周辺」研究集会
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘
    • Year and Date
      2009-12-13
  • [Presentation] 葉層の二次特性類の無限小微分 について2009

    • Author(s)
      足助太郎
    • Organizer
      「複素解析的ベクトル場・葉層構造とその周辺」研究集会
    • Place of Presentation
      龍谷大学セミナーハウスともいき荘
    • Year and Date
      2009-12-11
  • [Presentation] Embeddings of 2-toritransversal to linear vector fields on C^22009

    • Author(s)
      足助太郎
    • Organizer
      葉層構造と微分同相群研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2009-10-29
  • [Presentation] 多様体の微分同相群2008

    • Author(s)
      坪井俊
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-25
  • [Presentation] On the Fatou-Julia decomposition of transversally holomorphic foliations of complex codimension one2008

    • Author(s)
      Taro ASUKE
    • Organizer
      VIII International Colloquium on Differential Geometry
    • Place of Presentation
      Santiago de Compostela, Spain
    • Year and Date
      2008-07-11
  • [Presentation] On the uniform perfectness of the group of diffeomorphisms2008

    • Author(s)
      Takashi TSUBOI
    • Organizer
      VIII International Colloquium on Differential Geometry
    • Place of Presentation
      Santiago de Compostela, Spain
    • Year and Date
      2008-07-09
  • [Book] 幾何学III微分形式2008

    • Author(s)
      坪井俊
    • Total Pages
      248
    • Publisher
      東大出版会

URL: 

Published: 2014-08-29  

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