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Study on Homeomorphism Group

Research Project

Project/Area Number 14540093
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKyoto Sangyo University

Principal Investigator

FUKUI Kazuhiko  Kyoto Sangyo University, Faculty of Science, Professor, 理学部, 教授 (30065883)

Co-Investigator(Kenkyū-buntansha) USHITAKI Fumihiko  Kyoto Sangyo University, Faculty of Science, Associate Professor, 理学部, 助教授 (30232820)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
KeywordsLipschitz mapping / first homology of group / perfect / action of finite group / orbifold / foliated structure / リプシッツ同相群 / 1次元ホモロジー / 完全 / リプシッツ埋め込み / 境界をもつ多様体 / 余次元1コンパクト葉層 / ホモロジー / 多項式自己同型群 / コンパクト開リプシッツ位相
Research Abstract

(1) I organized the annual meeting "Homeomorphism Group and its related fields" (December of 2002, February of 2004 and December of 2004, (Kyoto Sangyo University) and I gave a talk (joint with K. Abe) everytime.
(2) I and T.Nakamura gave a talk entitled "Topological and algebraic properties of Lipschitz mappings" in the annual meeting of the Mathematical Society of Japan (September of 2002, Shimane University) and published a paper entitled "A topological property of Lipschitz mappings".
(3) I participated in "3^<rd> Workshop on Transformation Groups" (Poznan, Poland, August of 2003) and gave a talk entitled "Commutators of Lipschitz homeomorphisms preserving a geometric structure".
(4) I participated in the International Conference "Geometry and Foliations, Kyoto 2003" (Ryukoku University, Kyoto, September of 2003) and gave a talk entitled "Commutators of Lipschitz homeomorphisms".
(5) I gave a talk entitled "On the structure of the group of equivariant diffeomorphisms and application to foliation" in the meeting "Foliations and related fields" (Tokyo University, October of 2004).
(6) I (with K.Abe and T.Miura) submitted a paper entitled "On the first homology of the group of equivariant Lipschitz homeomorphisms".
(7) I and K.Abe submitted a paper entitled "On the first homology of automorphism groups of manifols with geometric structures".

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (15 results)

All 2005 2003 2002 Other

All Journal Article (9 results) Publications (6 results)

  • [Journal Article] A topological property of Lipschitz Mappings2005

    • Author(s)
      福井 和彦, 中村 太郎
    • Journal Title

      Topology and its Applications 148

      Pages: 143-152

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] A topological property of Lipschitz mappings2005

    • Author(s)
      Kazuhiko FUKUI, Taro Nakamura
    • Journal Title

      Topology and its Applications 148

      Pages: 143-152

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On the structure of the group of Lipschitz homeomorphisms and its subgroups, II2003

    • Author(s)
      阿部 孝順, 福井 和彦
    • Journal Title

      Jour.Math.Soc.Japan 55-4

      Pages: 947-956

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] On the structure of the group of Lipschitz homeomorphisms and its subgroups, II2003

    • Author(s)
      Kojun ABE, Kazuhiko FUKUI
    • Journal Title

      Jour.Math.Soc.Japan 55-4

      Pages: 947-956

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A note on the first homology of the group of polynomial automorphisms of the coordinate space2002

    • Author(s)
      福井 和彦, 平井 悦子
    • Journal Title

      Sci.Math.Japonicae 56-2

      Pages: 287-291

    • NAID

      10010239839

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Geometry of finite spaces and equivariant finite spaces2002

    • Author(s)
      河野 進, 牛瀧 文宏
    • Journal Title

      Current Trends in Transformation Groups(K-theory Monogragh Series)

      Pages: 53-63

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A note on the first homology of the group of polynomial automorphisms of the coordinate space2002

    • Author(s)
      Kazuhiko FUKUI, Etsuko HIRAI
    • Journal Title

      Sci.Math.Japonicae 56-2

      Pages: 287-291

    • NAID

      10010239839

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Geometry of finite spaces and equivariant finite spaces2002

    • Author(s)
      Susumu KONO, Fumihiro USHITAKI
    • Journal Title

      Current Trends in Transformation Groups

      Pages: 53-63

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Geometry of finite spaces and equivariant finite spaces2002

    • Author(s)
      河野 進, 牛瀧 文宏
    • Journal Title

      Current Trends in Transformation Groups(K-theory Monograpgh Series)

      Pages: 53-63

    • Related Report
      2004 Annual Research Report
  • [Publications] 福井 和彦: "A note on the first homology of the group of polynimial automorphisms of the coordinate space"Sci.Math.Japonicae. 56-2. 215-219 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] 阿部 孝順: "On the structure of the group of Lipschitz homeomorphisms and its subgroups II"J.Math.Soc.Japan. 55-4. 947-956 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 河野 進: "Geometry of finite spaces and equivariant finite spaces"Current Trends in Transformation Groups (K-theory Monograph Series). 53-63 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] 福井和彦, 平井悦子: "A note on the first homology of the group of polynomial automorphisms of the coordinate space"Sci.Math.Japonicae. 56-2. 287-291 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] 阿部孝順, 福井和彦: "On the structure of the group of Lipschitz homeomorphisms and its subgroups II"J.Math.Soc.Japan. (近刊).

    • Related Report
      2002 Annual Research Report
  • [Publications] 河野進, 牛瀧文宏: "Geometry of finite topological spaces and equivariant finite topological spaces"Current Trends in Transformation Groups (K-Monographs in Math.). 7. 53-63 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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