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On the homotopy properties of the Quillen complex of a symmetric group

Research Project

Project/Area Number 23540024
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionDokkyo Medical University

Principal Investigator

FUJITA Ryousuke  獨協医科大学, 医学部, 講師 (90270313)

Research Collaborator SAWABE Masato  千葉大学, 教育学部, 准教授
ODA Fumihito  近畿大学, 理工学部, 准教授
KONO Susumu  大阪大学, 理学研究科
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsキリン複体 / 部分群複体 / 順序複体 / ホモトピー性質 / 有限位相空間 / 有限T_0空間
Outline of Final Research Achievements

I obtained some new informations on homotopy properties of the Quillen complex of a genereal finite group, of course, including a symmetric group, from a topological point of view. As a result, it follows that the Quillen complex of a symmetric group is equivariant homotopy equivalent to the Quillen complex of its alternative group whose dimension is more than five. Besides, I contributed to create a new equivariant theory by finding the relation to the finite topological space theory.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (6 results)

All 2015 2014 2013 2011 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (5 results) (of which Invited: 2 results)

  • [Journal Article] On the Euler characteristic of a finite T_0 space2013

    • Author(s)
      Ryousuke Fujita
    • Journal Title

      Far East Journal of Mathematical Sciences

      Volume: 74 Pages: 87-103

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] On the finite space with a finite group action2015

    • Author(s)
      Ryousuke Fujita
    • Organizer
      RIMS研究集会「新しい変換群論の幾何」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-05-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] Quillen複体のトポロジー2014

    • Author(s)
      藤田亮介
    • Organizer
      変換群論セミナ―
    • Place of Presentation
      大阪大学理学研究科
    • Year and Date
      2014-06-28
    • Related Report
      2014 Annual Research Report
  • [Presentation] キリン複体の可縮性2011

    • Author(s)
      藤田亮介
    • Organizer
      大阪大学変換群論研究会
    • Place of Presentation
      大阪大学理学部数学教室
    • Related Report
      2011 Research-status Report
  • [Presentation] Some aspects of a finite T_0-G-space

    • Author(s)
      Ryousuke Fujita
    • Organizer
      RIMS研究集会「変換群のトポロジーとその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On the finite space with a finite group action

    • Author(s)
      Ryousuke Fujita
    • Organizer
      第30回代数的組合せ論シンポジウム
    • Place of Presentation
      静岡大学
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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