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Study of stability of fixed point sets in equivariant manifolds

Research Project

Project/Area Number 26400090
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

MORIMOTO Masaharu  岡山大学, 自然科学研究科, 教授 (30166441)

Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords同変多様体 / 変換群論 / 不動点集合 / 同変手術理論 / 同変コボルディズム / 変換群 / 群作用 / 多様体 / 同変手術 / s-同境 / バーンサイド環 / 有限群 / 手術理論 / Mackey 関手 / ギャップ条件 / 国際研究者交流 / ヨーロッパ
Outline of Final Research Achievements

Let G be a finite group and let F be a closed manifold satisfying a certain condition such as one of G-fixed point sets of smooth G-actions on disks or spheres. The purpose of this research project was to construct smooth G-actions with fixed point set F on a specified sequence X(1), X(2), X(3), ... of closed manifolds X(n), for example complex projective spaces, real projective spaces, and lens spaces. In the period of the present research project, we constructed smooth G-actions with fixed point set F for the group G being the alternating group of degree 5 or 6, on sequences of complex projective spaces, real projective spaces, and lens spaces, by means of the reflection method of G-framed maps and equivariant cobordisms, equivariant surgery theory, and s-cobordism theory.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (23 results)

All 2018 2017 2016 2015 2014 Other

All Journal Article (8 results) (of which Peer Reviewed: 6 results,  Acknowledgement Compliant: 5 results,  Open Access: 1 results) Presentation (12 results) (of which Int'l Joint Research: 1 results,  Invited: 2 results) Remarks (3 results)

  • [Journal Article] Cokernels of homomorphisms from Burnside rings to inverse limits II: G = C_{p^m} x C_{p^n}2018

    • Author(s)
      Masaharu Morimoto and Masafumi Sugimura
    • Journal Title

      Kyushu Journal of Mathematics

      Volume: 72

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cokernels of homomorphisms from Burnside rings to inverse limits2017

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      Canadian Mathematical Bulletin

      Volume: 60 Issue: 1 Pages: 165-172

    • DOI

      10.4153/cmb-2016-068-6

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Direct limits and inverse limits of Mackey functors2017

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      Journal of Algebra

      Volume: 470 Pages: 68-76

    • DOI

      10.1016/j.jalgebra.2016.09.002

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A necessary condition for the Smith equivalence of G-modules and its sufficiency2016

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      Mathematica Slovaca

      Volume: 66 Issue: 4 Pages: 979-998

    • DOI

      10.1515/ms-2015-0197

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] One-fixed-point actions on spheres and Smith sets2016

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      Osaka Journal of Mathematics

      Volume: 53

    • NAID

      120005941411

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On the V-transversality construction of equivariant framed maps2015

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1968

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Tangential representations of one-fixed-point actions on spheres and Smith equivalence2015

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 67 Issue: 1 Pages: 195-205

    • DOI

      10.2969/jmsj/06710195

    • NAID

      130004927762

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Tentative study on equivariant surgery obstructions: Fixed point sets of smooth A_5-actions2014

    • Author(s)
      Masaharu Morimoto
    • Journal Title

      数理解析研究所講究録

      Volume: 1922

    • Related Report
      2014 Research-status Report
    • Acknowledgement Compliant
  • [Presentation] Smooth one fixed point actions of S_5 on spheres2017

    • Author(s)
      森本 雅治,田村 俊輔
    • Organizer
      第44回変換群論シンポジウム
    • Related Report
      2017 Annual Research Report
  • [Presentation] Computation of quotient groups of inverse limits of Burnside rings2017

    • Author(s)
      森本 雅治
    • Organizer
      変換群を核とする代数的位相幾何学
    • Related Report
      2017 Annual Research Report
  • [Presentation] バーンサイド環の逆極限について12016

    • Author(s)
      森本 雅治
    • Organizer
      変換群論ワークショップ
    • Place of Presentation
      呉会員会館
    • Year and Date
      2016-03-10
    • Related Report
      2015 Research-status Report
  • [Presentation] Limits of the Burnside rings and their relations2016

    • Author(s)
      Masaharu Morimoto, Masafumi Sugimura
    • Organizer
      第43回変換群論シンポジウム
    • Place of Presentation
      姫路市民会館
    • Related Report
      2016 Research-status Report
  • [Presentation] Mackey 関手の極限について2016

    • Author(s)
      森本 雅治
    • Organizer
      日本数学会秋季総合文化会
    • Place of Presentation
      関西大学吹田キャンパス
    • Related Report
      2016 Research-status Report
  • [Presentation] 閉多様体のA_5-不動点集合としての実現2015

    • Author(s)
      森本 雅治
    • Organizer
      第42回変換群論シンポジウム
    • Place of Presentation
      金沢勤労者プラザ
    • Year and Date
      2015-11-28
    • Related Report
      2015 Research-status Report
  • [Presentation] The Burnside ring, equivariant framed maps, and the reflection method2015

    • Author(s)
      Masaharu Morimoto
    • Organizer
      Glances at Manifolds
    • Place of Presentation
      Jagiellonian University, Krakow, Poland
    • Year and Date
      2015-07-18
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 同変枠付き写像のV-横断正則構成について2015

    • Author(s)
      森本 雅治
    • 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
      2015-05-25
    • Related Report
      2015 Research-status Report
  • [Presentation] A module ω_F^* (―) over the Burnside ring2015

    • Author(s)
      森本 雅治
    • Organizer
      変換群論フォーラム研究会
    • Place of Presentation
      愛知県産業労働センター(名古屋市)
    • Year and Date
      2015-03-09
    • Related Report
      2014 Research-status Report
  • [Presentation] Topological equivalence relations on representation spaces2014

    • Author(s)
      Masaharu Morimoto
    • Organizer
      第41回変換群論シンポジウム
    • Place of Presentation
      蒲郡市民会館(蒲郡市 )
    • Year and Date
      2014-11-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Study of representation spaces from the viewpoint of algebraic/differential topology2014

    • Author(s)
      Masaharu Morimoto
    • Organizer
      DMV-PTM Conference 2014
    • Place of Presentation
      Poznan (Poland)
    • Year and Date
      2014-09-18
    • Related Report
      2014 Research-status Report
  • [Presentation] Tentative study on equivariant surgery obstructions: Fixed point sets of smooth A_5-actions2014

    • Author(s)
      Masaharu Morimoto
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2014-05-29
    • Related Report
      2014 Research-status Report
  • [Remarks] Published Papers

    • URL

      http://www.ems.okayama-u.ac.jp/appl/morimoto/publmme.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] List of Published Papers

    • URL

      http://www.ems.okayama-u.ac.jp/appl/morimoto/publmme.html

    • Related Report
      2016 Research-status Report
  • [Remarks] セミナー案内 講演録

    • URL

      http://www.ems.okayama-u.ac.jp/appl/morimoto/Seminar/

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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