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Cohomology of mapping class groups, Coxeter groups and Artin groups

Research Project

Project/Area Number 26400077
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

Akita Toshiyuki  北海道大学, 理学研究院, 准教授 (30279252)

Co-Investigator(Kenkyū-buntansha) 吉永 正彦  北海道大学, 理学研究院, 准教授 (90467647)
Co-Investigator(Renkei-kenkyūsha) SATOH Takao  東京理科大学, 理学部第二部, 准教授 (70533256)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsトポロジー / Coxeter群 / Artin群 / 群のコホモロジー / カンドル / 交代群 / crossed module / 写像類群 / 消滅定理
Outline of Final Research Achievements

We studied group cohomology of Coxeter groups, Artin groups and related groups. As for Coxeter groups, we obtain (1) a vanishing theorem for the p-local homology of Coxeter groups (2) a vanishing theorem for the mod p cohomology of alternating subgroups of finite Coxeter groups. As for Artin groups (3) we determined the second mod 2 homology of arbitrary Artin groups. (2) and (3) are joint works with Ye Liu. Finally, we proved that the adjoint group of an arbitrary Coxeter quandle is both a central extension of a Coxeter group W by a free abelian group and a semi-direct product of the commutator subgroup of a Coxeter group W and a free abelian group.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (14 results)

All 2017 2016 2015 2014

All Journal Article (3 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 7 results)

  • [Journal Article] Vanishing ranges for the mod p cohomology of alternating subgroups of Coxeter groups2017

    • Author(s)
      Akita, Toshiyuki; Liu, Ye
    • Journal Title

      Journal of Algebra

      Volume: 473 Pages: 132-141

    • DOI

      10.1016/j.jalgebra.2016.11.005

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A vanishing theorem for the p-local homology of Coxeter groups2016

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Bulletin of the London Mathematical Society

      Volume: 48 Issue: 6 Pages: 945956-945956

    • DOI

      10.1112/blms/bdw063

    • NAID

      120006366495

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Vanishing theorems for the homology of Coxeter groups and their alternating subgroups2015

    • Author(s)
      秋田利之
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1967 Pages: 53-58

    • Related Report
      2015 Research-status Report
  • [Presentation] On the mod p cohomology of Coxeter groups and their alternating subgroups2016

    • Author(s)
      Toshiyuki Akita
    • Organizer
      ホモトピー論シンポジウム
    • Place of Presentation
      県立広島大学サテライトキャンパス(広島県・広島市)
    • Year and Date
      2016-11-12
    • Related Report
      2016 Annual Research Report
  • [Presentation] Cohomology of Coxeter groups and related groups2016

    • Author(s)
      Toshiyuki Akita
    • Organizer
      Perspectives on arrangements and configuration spaces
    • Place of Presentation
      ピサ(イタリア)
    • Year and Date
      2016-09-08
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Crossed modules and Artin groups2016

    • Author(s)
      Toshiyuki Akita
    • Organizer
      京都大学代数トポロジーセミナー
    • Place of Presentation
      京都大学理学部(京都府・京都市)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Second mod 2 homology of Artin groups2016

    • Author(s)
      Toshiyuki Akita
    • Organizer
      東京大学火曜トポロジーセミナー
    • Place of Presentation
      東京大学数理科学研究科(東京都・目黒区)
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] Homological aspects of Coxeter groups2015

    • Author(s)
      秋田利之
    • Organizer
      東京理科大学理工学部数学教室談話会
    • Place of Presentation
      東京理科大学理工学部(千葉県・野田市)
    • Year and Date
      2015-11-06
    • Related Report
      2015 Research-status Report
  • [Presentation] Vanishing theorems for the homology of Coxeter groups and their alternating subgroups2015

    • Author(s)
      秋田利之
    • Organizer
      研究集会「有限群のコホモロジー論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2015-02-19
    • Related Report
      2014 Research-status Report
  • [Presentation] Vanishing theorems for the homology of Coxeter groups and their alternating subgroups2015

    • Author(s)
      秋田利之
    • Organizer
      Workshop and Seminar on Topological Combinatorics and Related Topics
    • Place of Presentation
      カセサート大学(タイ)
    • Year and Date
      2015-01-07
    • Related Report
      2014 Research-status Report
  • [Presentation] Vanishing theorems for p-local homology of Coxeter groups and their alternating subgroups2014

    • Author(s)
      秋田利之
    • Organizer
      東京大学トポロジー火曜セミナー
    • Place of Presentation
      東京大学数理科学研究科(東京都目黒区)
    • Year and Date
      2014-10-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Vanishing theorems for p-local homology groups of Coxeter groups and their alternating subgroups2014

    • Author(s)
      秋田利之
    • Organizer
      The 1st Workshop of JSPS-MAE Sakura Program "Geometry and Combinatorics of Hyperplane Arrangements and Related Problems"
    • Place of Presentation
      北海道大学理学研究院(北海道札幌市)
    • Year and Date
      2014-09-02
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Vanishing theorem for p-local homology of Coxeter groups2014

    • Author(s)
      秋田利之
    • Organizer
      九州大学トポロジー金曜セミナー
    • Place of Presentation
      九州大学数理学研究院(福岡県福岡市)
    • Year and Date
      2014-06-06
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Coxeter群のホモロジーのp-primary componentについて2014

    • Author(s)
      秋田利之
    • Organizer
      研究集会「変換群の位相幾何と代数構造」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2014-05-30
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2018-03-22  

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