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Rigidity and fixed-point property of finitely generated groups

Research Project

Project/Area Number 21540062
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKeio University (2010-2011)
Tohoku University (2009)

Principal Investigator

IZEKI Hiroyasu  慶應義塾大学, 理工学部, 教授 (90244409)

Co-Investigator(Renkei-kenkyūsha) NAYATANI Shin  名古屋大学, 大学院・多元数理科学研究科, 教授 (70222180)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords有限生成群 / 剛性 / 固定点性質 / 調和写像 / ランダム群 / 非正曲率空間
Research Abstract

A group G is said to have rigidity, if the space accepting the action of G is very restrictive. A group G is said to have fixed-point property for a space Y, if every action of G fixes a point in Y. Recent development of mathematical research suggests that there are plenty of groups having rigidity. We proved that, in a certain model, groups have strong fixed-point property with high probability.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (15 results)

All 2011 2010 2009 Other

All Journal Article (10 results) (of which Peer Reviewed: 5 results) Presentation (5 results)

  • [Journal Article] An approach to superrigidity and fixed-point theorems via harmonic maps2010

    • Author(s)
      Hiroyasu Izeki and Shin Nayatani
    • Journal Title

      Amer. Math. Soc. Transl

      Volume: 2 Pages: 135-160

    • Related Report
      2011 Final Research Report
  • [Journal Article] A fixed-point property of finitely generated groups and an energy of equivariant maps2010

    • Author(s)
      Hiroyasu Izeki
    • Journal Title

      Probabilistic Approach to Geometry

      Volume: 57 Pages: 171-188

    • Related Report
      2011 Final Research Report
  • [Journal Article] A fixed-point property of finitely generated groups and an energy of equivariant maps2010

    • Author(s)
      Hiroyasu Izeki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 57 Pages: 171-188

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An approach to superrigidity and fixed-point property theorems via harmonic maps2010

    • Author(s)
      Hiroyasu Izeki, Shin Nayatani
    • Journal Title

      Amer.Math.Soc.Transl.(2)

      Volume: 230 Pages: 135-160

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A fixed-point property of finitely generated groups and an energy of equivariant maps2010

    • Author(s)
      H.Izeki
    • Journal Title

      Advanced Studies in Pure Mathematics 57

      Pages: 171-188

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fixed-point property of random groups2009

    • Author(s)
      Hiroyasu Izeki, Takefumi Kondo, and Shin Nayatani
    • Journal Title

      Annals of Global Analysis and Geom

      Volume: 35 Pages: 363-379

    • Related Report
      2011 Final Research Report
  • [Journal Article] Fixed-point property of random groups2009

    • Author(s)
      H.Izeki, T.Kondo, S.Nayatani
    • Journal Title

      Annals of Global Analysis and Geometry 35

      Pages: 363-379

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Fixed-point property of random qutients by plain words

    • Author(s)
      Hiroyasu Izeki
    • Journal Title

      Groups, Geometry, and Dynamics

      Volume: (掲載決定)

    • Related Report
      2011 Final Research Report
  • [Journal Article] N-step energy of maps and fixed-point property of random groups, Groups, Geometry

    • Author(s)
      Hiroyasu Izeki, Takefumi Kondo, and Shin Nayatani
    • Journal Title

      Groups, Geometry, and Dynamics

      Volume: (掲載決定)

    • Related Report
      2011 Final Research Report
  • [Journal Article] N-step energy of maps and fixed-point property of random groups

    • Author(s)
      H.Izeki, T.Kondo, S.Nayatani
    • Journal Title

      Groups, Geometry, and Dynamics

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] ランダム群の固定点性質2011

    • Author(s)
      井関裕靖
    • Organizer
      仙台シンポジウム2011
    • Place of Presentation
      東北大学大学院情報科学研究科
    • Year and Date
      2011-08-18
    • Related Report
      2011 Final Research Report
  • [Presentation] ランダム群の固定点性質2011

    • Author(s)
      井関裕靖
    • Organizer
      仙台シンポジウム2011
    • Place of Presentation
      東北大学大学院情報科学研究科(招待講演)
    • Year and Date
      2011-08-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 同変写像のエネルギーと有限生成群の剛性2010

    • Author(s)
      井関裕靖
    • Organizer
      福岡微分幾何学研究会
    • Place of Presentation
      福岡大学
    • Year and Date
      2010-10-09
    • Related Report
      2011 Final Research Report
  • [Presentation] ランダム群の固定点性質2009

    • Author(s)
      井関裕靖
    • Organizer
      第56回幾何学シンポジウム
    • Place of Presentation
      佐賀大学
    • Year and Date
      2009-08-28
    • Related Report
      2011 Final Research Report
  • [Presentation] ランダム群の固定点性質2009

    • Author(s)
      井関裕靖
    • Organizer
      第56回幾何学シンポジウム
    • Place of Presentation
      佐賀
    • Year and Date
      2009-08-28
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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