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Coho mology of discrete groups and characteristic classes of flat bundles

Research Project

Project/Area Number 20340008
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

AKITA Toshiyuki  北海道大学, 大学院・理学研究院, 准教授 (30279252)

Co-Investigator(Kenkyū-buntansha) OHMOTO Toru  北海道大学, 大学院・理学研究院, 准教授 (20264400)
WATANABE Tadayuki  北海道大学, 大学院・理学研究院, 助教 (70467447)
YOSHIDA Tomoyuki  北海道大学, 大学院・理学研究院, 教授 (30002265)
Co-Investigator(Renkei-kenkyūsha) KURIBAYASHI Katsuhiko  信州大学, 理学部, 教授 (40249751)
YAGITA Nobuaki  茨城大学, 教育学部, 教授 (20130768)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥12,480,000 (Direct Cost: ¥9,600,000、Indirect Cost: ¥2,880,000)
Fiscal Year 2011: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2009: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Keywordsコホモロジー / 特性類 / 線型表現 / 写像類群 / 分岐被覆 / 離散群 / 群のコホモロジー / 平坦束 / Mackey 函手 / トポロジー / 分類空間 / Mackey函手 / 幾何学
Research Abstract

We construct a functorial framework to deal with all finite transformation groups on closed surfaces (Galois covers on closed surfaces) simultaneously. Characteristic classes associated with such transformation groups, Mumford-Morita-Miller classes and Newton classes, are shown to be natural transformations of functors. These characteristic classes are shown to satisfy Riemann-Roch type formulae.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (42 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (23 results) (of which Peer Reviewed: 22 results) Presentation (18 results) Remarks (1 results)

  • [Journal Article] 1-loop graphs and configuration space integral for embedded spaces2012

    • Author(s)
      Keiichi Sakai, Tadayuki Watanabe
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: 152 Issue: 3 Pages: 497-533

    • DOI

      10.1017/s0305004111000429

    • NAID

      120005228644

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity for Mumford-Morita-Miller classes of surface symmetries2011

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Publications of the Research Institute for Mathematical Sciences

      Volume: 47 Issue: 4 Pages: 897-909

    • DOI

      10.2977/prims/55

    • NAID

      110008747020

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity for Mumford-Morita-Miller classes of surface symmetries2011

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Publ.RIMS Kyoto Univ. 印刷中

    • NAID

      110008747020

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Periodicity for Mumford-Morita-Miller classes for surface symmetries2011

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Publ.RIMS Kyoto Univ.

      Volume: 印刷中

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 1-loop graphs and configuration space integral for embedded spaces2011

    • Author(s)
      Keiichi Sakai, Tadayuki Watanabe
    • Journal Title

      Math.Proc.Cambridge Phil.Soc.

      Volume: 印刷中

    • NAID

      120005228644

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Kontsevich's characteristic classes for higher dimensional sphere bundles. II. Higher claases2009

    • Author(s)
      Tadayuki Watanabe
    • Journal Title

      Journal of Topology

      Volume: 2 Issue: 3 Pages: 624-660

    • DOI

      10.1112/jtopol/jtp024

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Kontsevich's characteristic classes for higher dimensional sphere bundles. I. The simplest class2009

    • Author(s)
      Tadayuki Watanabe
    • Journal Title

      Mathematische Zeitschrift

      Volume: 262 Issue: 3 Pages: 683-712

    • DOI

      10.1007/s00209-008-0396-4

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Thom polynomial and around, RIMS Kokyuroku Bessatsu B112009

    • Author(s)
      Toru Ohmoto
    • Journal Title

      New Trends in Combinatorial Representation Theory (eds. S. Arikiand M. Okado)

      Pages: 75-86

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 特異点の数え上げと同変Chern類2009

    • Author(s)
      大本亨
    • Journal Title

      数学

      Volume: 61 Pages: 21-39

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Kontsevich's characteristic classes for higher-dimensional sphere bundles. II. Higher classes.2009

    • Author(s)
      Tadayuki Watanabe
    • Journal Title

      J.Topol. 2

      Pages: 624-660

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On mod p Riemann-Roch formulae for mapping class groups2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 52 Pages: 111-118

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A formula for the Euler characteristics of evendimensional triangulated manifolds2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 136 Issue: 07 Pages: 2571-2573

    • DOI

      10.1090/s0002-9939-08-09148-x

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Nariya Kawazumi, Integral Riemann-Roch formulae forcyclic subgroups of mapping classgroups2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: 144 Issue: 2 Pages: 411-421

    • DOI

      10.1017/s0305004107001016

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions of orbifold Chern classes I : Symmetric Products2008

    • Author(s)
      Toru Ohmoto
    • Journal Title

      Mathematical Proceedings of the Cambridge Philosophical Society

      Volume: 144 Issue: 2 Pages: 423-438

    • DOI

      10.1017/s0305004107000898

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Surface symmetries, homology representations, and group cohomology2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      数理解析研究所講究録

      Volume: 1581 Pages: 103-108

    • NAID

      120001442850

    • Related Report
      2011 Final Research Report
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

    • Author(s)
      Toshiyuki Akita, Nariya Kawazumi
    • Journal Title

      Math.Proc.Cambridge Phil.Soc. 144

      Pages: 411-421

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On mod p Riemann-Roch formulae for mapping class groups2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Advanced Studies in Pure Math. 52

      Pages: 111-118

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Generating functions of orbifold Chern classes I : Symmetric Products2008

    • Author(s)
      Toru Ohmoto
    • Journal Title

      Math.Proc.Cambridge Phil.Soc. 144

      Pages: 423-438

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Integral Ricmann-Roch formulae for cyclic subgroups of mappina class groups2008

    • Author(s)
      Toshiyuki Akita. Nariva Kawazumi
    • Journal Title

      Mathcmatical Proceedings of the Cambridge Philosophical Society 144

      Pages: 411-421

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A formula for the Euler characteristics of even dimensional manifolds2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Proceedings of the American Mathematical Society 136

      Pages: 2571-2573

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On mod p Riemann-Roch formulae for mapping class groups2008

    • Author(s)
      Toshiyuki Akita
    • Journal Title

      Advanced Studies in Pure Mathematics 52

      Pages: 111-118

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Vassiliev type invariants for generic mappings, revisited

    • Author(s)
      Toru Ohmoto
    • Journal Title

      Contemporary Mathematics, AMS

      Volume: (印刷中)(掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on Chern-Schwartz-MacPherson class

    • Author(s)
      Toru Ohmoto
    • Journal Title

      Proceedings of the 5th Franco-Japanese Singularities, Strasbourg

      Volume: (印刷中)(掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Surface symmetries and equivariant characteristic classes2012

    • Author(s)
      Toshiyuki Akita
    • Organizer
      Topology of Singularities and Related Topics III (JSPS-VAST Japan-Vietnam Bilateral Joint Projects)
    • Place of Presentation
      University of Dalat, Dalat, ベトナム
    • Year and Date
      2012-03-29
    • Related Report
      2011 Final Research Report
  • [Presentation] Surface symmetries and equivariant characteristic classes2012

    • Author(s)
      Toshiyuki Akita
    • Organizer
      Topology of Singularities and Related Topics III
    • Place of Presentation
      ダラット大学(ベトナム)(招待講演)
    • Year and Date
      2012-03-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Singular Chern class and degree formula2012

    • Author(s)
      Toru Ohmoto
    • Organizer
      第7回代数・解析・幾何セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2012-02-15
    • Related Report
      2011 Final Research Report
  • [Presentation] Singular Chern class and degree formula2012

    • Author(s)
      Toru Ohmoto
    • Organizer
      The 7th Kagoshima Algebro-Analysis-Geometry Seminar
    • Place of Presentation
      鹿児島大学理学部(招待講演)
    • Year and Date
      2012-02-15
    • Related Report
      2011 Annual Research Report
  • [Presentation] Obstructions forπ1 of the space of pseudo-isotopies of disks in non-stable range2011

    • Author(s)
      Tadayuki Watanabe
    • Organizer
      The 4th East Asian Conference on Algebraic Topology
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2011-12-09
    • Related Report
      2011 Final Research Report
  • [Presentation] Obstructions for π1 of the space of pseudo-isotopies of disks in non-stable range2011

    • Author(s)
      Tadayuki Watanabe
    • Organizer
      The 4th East Asian Conference on Algebraic Topology
    • Place of Presentation
      東京大学大学院数理科学研究科(招待講演)
    • Year and Date
      2011-12-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Surface symmetry and cohomology of finite groups2011

    • Author(s)
      Toshiyuki Akita
    • Organizer
      Seminarios de Topologia
    • Place of Presentation
      ICMC-USP, Sao Carlos, ブラジル
    • Year and Date
      2011-09-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Surface symmetry and cohomology of finite groups2011

    • Author(s)
      Toshiyuki Akita
    • Organizer
      Seminarios de Topologia, ICMC-USP
    • Place of Presentation
      サンパウロ大学(ブラジル)(招待講演)
    • Year and Date
      2011-09-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Thom polynomial associated to the Milnor number of ICSC.2011

    • Author(s)
      Toru Ohmoto
    • Organizer
      Banach Center Conference, Workshop on Singularities in Geometry and Application
    • Place of Presentation
      ポーランド
    • Year and Date
      2011-05-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Thom polynomial associated to the Milnor number of ICSC2011

    • Author(s)
      Toru Ohmoto
    • Organizer
      Banach Center Conference, Workshop on Singularities in Geometry and Application
    • Place of Presentation
      バナッハッセンター(ポーランド)(招待講演)
    • Year and Date
      2011-05-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Mackey functors associated with surface symmetries2011

    • Author(s)
      Toshiyuki Akita
    • Organizer
      第6回代数・解析・幾何セミナー
    • Place of Presentation
      鹿児島大学理学部
    • Year and Date
      2011-02-15
    • Related Report
      2011 Final Research Report 2010 Annual Research Report 2010 Self-evaluation Report
  • [Presentation] Chern class for singular spaces2011

    • Author(s)
      Toru Ohmoto
    • Organizer
      JSPS-VAST Japan-Vietnam Bilateral Joint Projects Topology of singularities and related topics II
    • Place of Presentation
      東北大学大学院理学研究科
    • Year and Date
      2011-01-06
    • Related Report
      2011 Final Research Report 2010 Self-evaluation Report
  • [Presentation] Vassiliev type invariants revisited2010

    • Author(s)
      Toru Ohmoto
    • Organizer
      The 11th International Workshop on Real and Complex Singularities
    • Place of Presentation
      Instituto de Ciencias Matematicase de Computacao, ブラジル
    • Year and Date
      2010-07-27
    • Related Report
      2011 Final Research Report
  • [Presentation]2010

    • Author(s)
      大本亨
    • Organizer
      The 11th International Workshop on Real and Complex Singularities
    • Place of Presentation
      Instituto de Ciencias Matematicas e de Computacao(ブラジル)
    • Year and Date
      2010-07-27
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Cohomology of finite groups and characteristic classes2009

    • Author(s)
      秋田利之
    • Organizer
      京都大学数学教室談話会
    • Place of Presentation
      京都大学
    • Year and Date
      2009-12-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Kontsevich's graph characteristic classes of smooth bundles2009

    • Author(s)
      Tadayuki Watanabe
    • Organizer
      Quantum algebra related to various topological field theories in geometries
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-02-16
    • Related Report
      2011 Final Research Report
  • [Presentation]2009

    • Author(s)
      渡邉忠之
    • Organizer
      Quantum algebra related to various topological field theories in geometries
    • Place of Presentation
      京都大学理学部
    • Year and Date
      2009-02-16
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Surface symmetries and group cohomology2008

    • Author(s)
      秋田利之
    • Organizer
      福岡微分幾何研究会
    • Place of Presentation
      福岡大学セミナーハウス
    • Year and Date
      2008-11-23
    • Related Report
      2010 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.math.sci.hokudai.ac.jp/~akita/

    • Related Report
      2011 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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