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2013 Fiscal Year Final Research Report

Study of deformation of group actions from various viewpoints

Research Project

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Project/Area Number 22684003
Research Category

Grant-in-Aid for Young Scientists (A)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionKyoto University

Principal Investigator

ASAOKA Masayuki  京都大学, 理学(系)研究科(研究院), 准教授 (10314832)

Project Period (FY) 2010-04-01 – 2014-03-31
Keywords群作用 / 力学系
Research Abstract

We studied deformation of group actions from various viewpoints, mainly from geometric and dynamical view points. From geometric side, we proved that a natural conformal action on the sphere admits only conformal deformation. We also applied the method used in this result to another action on the torus. We proved an action on the torus which preserves a geometric structure admits only deformation which preserves the same type of geometric structure. From dynamical side, we reinterpreted several known rigidity results on group actions from the viewpoint of expansion property of the actions

  • Research Products

    (21 results)

All 2013 2012 2011 2010

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (16 results) (of which Invited: 14 results)

  • [Journal Article] On the large deviationrates on non-entropy-approachable measure2013

    • Author(s)
      M.Asaoka and K.Yamamoto
    • Journal Title

      Disc. And Conti. Dyn. Sys

      Volume: vol.33 Pages: 4401-4410

    • Peer Reviewed
  • [Journal Article] Rigidity of certain solvable actions on the sphere2012

    • Author(s)
      M.Asaoka
    • Journal Title

      Geom. and Topology

      Volume: 16, no.3 Pages: 1835-1857

    • Peer Reviewed
  • [Journal Article] Homotopy classes of total foliations and bi-contact structures on three-manifolds2012

    • Author(s)
      M. Asaoka, E.Dufraine, and T.Noda
    • Journal Title

      Comm. Math. Helv

      Volume: 87, no.2 Pages: 271-302

    • Peer Reviewed
  • [Journal Article] Non-homogeneous locally free actions of the affine group2012

    • Author(s)
      M.Asaoka
    • Journal Title

      Ann. of Math

      Volume: 175, no.1 Pages: 1-21

    • Peer Reviewed
  • [Journal Article] Remark on dynamical morse in- equality2011

    • Author(s)
      M.Asaoka, T. Fukaya, and M. Tsukamoto
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci

      Volume: 87, no.9 Pages: 178-182

    • Peer Reviewed
  • [Presentation] A cocycle rigidity lemma for Baumslag-Solitar actions and its applica -tions2013

    • Author(s)
      M. Asaoka
    • Organizer
      Geometric Geometry and Foliations 2013
    • Place of Presentation
      東京大学大学院数理科学研究
    • Year and Date
      2013-09-09
    • Invited
  • [Presentation] A cocycle rigidity lemma for Baumslag-Solitar actions and its applications2013

    • Author(s)
      M. Asaoka
    • Organizer
      Geometric Group Theory-Kyoto 2013
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2013-07-19
    • Invited
  • [Presentation] Growth of critical poiints in one-dimensional lattice systems I2013

    • Author(s)
      M. Asaoka
    • Organizer
      Dynamics, Entropy and Semialgebraic Sets
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2013-07-11
    • Invited
  • [Presentation] アノソフ力学系と群作用の剛性問題2013

    • Author(s)
      浅岡正幸
    • Organizer
      日本数学会年会
    • Year and Date
      2013-03-21
    • Invited
  • [Presentation] Growth of critical points in one-dimensional lattice systems2013

    • Author(s)
      M. Asaoka
    • Organizer
      Descrete geometry and dynamical systems
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2013-01-24
    • Invited
  • [Presentation] Growth of critical points in one -dimensional lattice systems2012

    • Author(s)
      M. Asaoka
    • Organizer
      力学系とその周辺分野
    • Place of Presentation
      京都大学 数理解析研究所
    • Year and Date
      2012-07-11
    • Invited
  • [Presentation] Rigidity of certain solvable actions on the sphere2012

    • Author(s)
      M. Asaoka
    • Organizer
      Foliations 2012
    • Place of Presentation
      Univsersity of Lodz, Lodz (Poland)
    • Year and Date
      2012-06-28
    • Invited
  • [Presentation] Local rigidity of homogeneous actions of parabolic subgroups of rank-one Lie groups Anosov systems2012

    • Author(s)
      M. Asaoka
    • Organizer
      CIRM Luminy
    • Place of Presentation
      Marseille (France)
    • Year and Date
      2012-06-19
    • Invited
  • [Presentation] Rigidity of an abelian-by-cyclic action on the n-sphere2012

    • Author(s)
      M. Asaoka
    • Organizer
      Geometric group theory and K-theory (RIMS International Camp on Discrete geometry)
    • Place of Presentation
      鳥羽シーサイドホテル, 鳥羽市
    • Year and Date
      2012-06-14
    • Invited
  • [Presentation] Rigidity of certain solvable actions on the sphere2012

    • Author(s)
      M. Asaoka
    • Organizer
      ICTP-ESF School and Conference in Dynamical Systems, ICTP
    • Place of Presentation
      Trieste (Italy)
    • Year and Date
      2012-05-28
    • Invited
  • [Presentation] Weak form of local rigidity of ce rtain solvable actions2011

    • Author(s)
      M. Asaoka
    • Organizer
      力学系とトポロジーのフロンティア (Frontiers in Dynamical systems and Topology)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-11-22
  • [Presentation] Local rigidity of certain solvable actions2011

    • Author(s)
      M. Asaoka
    • Organizer
      多様体の平面場と微分同相群 2011 (Plane Fields on Manifolds and Diffeomorphisms Groups 2011)
    • Place of Presentation
      東京大学玉原セミナーハウス
    • Year and Date
      2011-11-02
  • [Presentation] 滑らかな群作用の剛性と変形2011

    • Author(s)
      浅岡正幸
    • Organizer
      第58回幾何学シンポジウム
    • Place of Presentation
      山口大学吉田キャンパス
    • Year and Date
      2011-08-28
    • Invited
  • [Presentation] Rigidity of certain solvable group action on the 2-sphere, Beyond Uniform Hyperbolicity2011

    • Author(s)
      M. Asaoka
    • Organizer
      CIRM
    • Place of Presentation
      Marseille, France
    • Year and Date
      2011-06-09
    • Invited
  • [Presentation] Parameter rigidity and leafwise cohomology2011

    • Author(s)
      M. Asaoka
    • Organizer
      Geometry and Analysis
    • Place of Presentation
      京都大学大学院理学研究科
    • Year and Date
      2011-03-09
    • Invited
  • [Presentation] Rigidity and Flexibility of group actions. Various Aspects of Dynami- cal Systems - ICM 2010 Satellite Conference2010

    • Author(s)
      M. Asaoka
    • Organizer
      The Maharaja Sayajirao University of Baroda
    • Place of Presentation
      Vadodara, India
    • Year and Date
      2010-09-01
    • Invited

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Published: 2015-07-16  

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