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2010 Fiscal Year Self-evaluation Report

Groups of diffeomorphisms

Research Project

  • PDF
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  The University of Tokyo, 大学院・数理科学研究科, 教授 (40114566)

Project Period (FY) 2008 – 2012
Keywords微分トポロジー
Research Abstract

微分同相群および(連結成分の群である)写像類群への表現、これらの群の様々な部分群の配置、微分同相群や写像類群のホモロジー的、力学系的、幾何的不変量を研究し、様々な多様体上の構造を解明することを目的とし、そのために、様々な構造を保つ微分同相群の位相およびその分類空間の位相、微分同相群の離散部分群の変形、微分同相群のリー部分群の力学系理論的性質、微分同相群に付随する亜群、写像類群の分類空間の性質、微分同相群の力学系的不変量と幾何的不変量に焦点を絞り、微分同相群および多様体の構造の不変量の発見、新しい研究手法を開発を期するとともに研究相互の関連を明らかにする。

  • Research Products

    (11 results)

All 2011 2010 2009 2008

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (5 results) Book (1 results)

  • [Journal Article] Godbillon-Vey class of transversely holomorphic foliations.2010

    • Author(s)
      Taro Asuke
    • Journal Title

      MSJ memoirs 24

      Pages: 1-130

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

    • Author(s)
      Shuhei Hayashi
    • Journal Title

      Proceedings of American Mathematical Society 138

      Pages: 1371-1385

    • Peer Reviewed
  • [Journal Article] Classifying spaces for groupoid structures2009

    • Author(s)
      Takashi Tsuboi
    • Journal Title

      Contemporary Mathematics 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 49

      Pages: 601-651

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

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Advanced Studies in Pure Mathematics 52

      Pages: 383-400

    • Peer Reviewed
  • [Presentation] AC^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
      2011-01-01
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Workshop 'Teichmueller Theory'
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach.
    • Year and Date
      2010-12-03
  • [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] 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
      総合講演,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
  • [Book] 幾何学III微分形式2008

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

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Published: 2012-02-13   Modified: 2016-04-21  

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