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Structure of mapping class groups and topology of 4-manifolds

Research Project

Project/Area Number 21540079
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionTokyo Institute of Technology (2011-2013)
Osaka University (2009-2010)

Principal Investigator

ENDO Hisaaki  東京工業大学, 理工学研究科, 教授 (20323777)

Co-Investigator(Kenkyū-buntansha) KIKUCHI Kazunori  大阪大学, 大学院理学研究科, 講師 (40252572)
Project Period (FY) 2009-04-01 – 2013-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords4次元多様体 / 写像類群 / Lefschetzファイバー空間 / モノドロミー / 有理ブローダウン / 微分構造 / ファイバー和 / チャート表示 / 4次元多様体 / 超楕円性 / 安定化 / トポロジー / 幾何学 / BLF / 国際情報交換 / アメリカ / 群の表示 / quandle / コサイクル
Research Abstract

It is often more difficult to examine low dimensional manifolds (3-manifolds and 4-manifolds) than to examine higher dimensional manifolds in topology. We studied the topology of 4-manifolds in this research project. In particular, we investigated Lefschetz fibrations, which are 4-manifolds consisting of infinitely many (possibly singular) surfaces (2-manifolds). We make use of mapping class groups of surfaces, which are algebraic objects related with surfaces, to describe Lefschetz fibrations. We found several close relations between some data in mapping class groups and smooth structures on total spaces of Lefschetz fibrations in this research.

Report

(5 results)
  • 2013 Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (24 results)

All 2014 2013 2012 2011 2010 Other

All Journal Article (6 results) (of which Peer Reviewed: 6 results) Presentation (15 results) (of which Invited: 2 results) Remarks (3 results)

  • [Journal Article] Chart description for hyperelliptic Lefschetz fibrations and their stabilization2014

    • Author(s)
      Hisaaki Endo and Seiichi Kamada
    • Journal Title

      Topology and its Applications

      Volume: 印刷中

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monodromy substitutions and rational blowdowns2011

    • Author(s)
      Hisaaki Endo, Thomas E. Mark, and Jeremy Van Horn-Morris
    • Journal Title

      Journal of Topology

      Volume: Vol. 4 Issue: 1 Pages: 227-253

    • DOI

      10.1112/jtopol/jtq041

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Monodromy substitutions and rational blowdowns2011

    • Author(s)
      H.Endo, T.E.Mark, J.Van Horn-Morris
    • Journal Title

      Journal of Topology

      Volume: Vol.4(掲載確定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Gurtas, Lantern relations and rational blowdowns2010

    • Author(s)
      Hisaaki Endo and Yusuf Z
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: Vol. 138 Issue: 3 Pages: 1131-1142

    • DOI

      10.1090/s0002-9939-09-10128-4

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Lantern relations and rational blowdowns2010

    • Author(s)
      H.Endo, Y.Z.Gurtas
    • Journal Title

      Proceedings of the American Mathematical Society 138

      Pages: 1131-1142

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Chart description for hyperelliptic Lefschetz fibrations and their stabilization

    • Author(s)
      Hisaaki Endo and Seiichi Kamada
    • Journal Title

      Topology and its Applications

      Volume: (掲載決定)

    • URL

      http://arxiv.org/abs/1306.2707

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Presentation] 超楕円的Lefschetzファイバー空間の安定同型類について2013

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「Hurwitz actionとその周辺」
    • Place of Presentation
      群馬大学荒牧キャンパス教育学部C棟C201
    • Year and Date
      2013-01-05
    • Related Report
      2013 Final Research Report
  • [Presentation] 超楕円的Lefschetzファイバー空間の安定同型類について2013

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「Hurwitz actionとその周辺」
    • Place of Presentation
      群馬大学教育学部
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Lefschetzファイバー空間のファイバー和による安定化について2012

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「リーマン面に関連する位相幾何学」
    • Place of Presentation
      東京大学大学院数理科学研究科大講義室
    • Year and Date
      2012-09-02
    • Related Report
      2013 Final Research Report
  • [Presentation] Lefschetzファイバー空間の安定化について2012

    • Author(s)
      遠藤久顕
    • Organizer
      トポロジーセミナー
    • Place of Presentation
      東京工業大学西8号館W1101セミナー室
    • Year and Date
      2012-04-11
    • Related Report
      2013 Final Research Report
  • [Presentation] Lefschetzファイバー空間のファイバー和による安定化について2012

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「リーマン面に関連する位相幾何学」
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Irreducle Lefschetz fibrations2011

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「タイヒミュラー理論によるレフシェッツファイバーの研究の新展開」
    • Place of Presentation
      アピカルイン京都・楓の間
    • Year and Date
      2011-12-17
    • Related Report
      2013 Final Research Report
  • [Presentation] Constructions and modifications of Lefschetz fibrations2011

    • Author(s)
      遠藤久顕
    • Organizer
      幾何セミナー
    • Place of Presentation
      大阪大学理学部E棟E301
    • Year and Date
      2011-12-05
    • Related Report
      2013 Final Research Report
  • [Presentation] Lefschetzファイバー空間の構成と改変について2011

    • Author(s)
      遠藤久顕
    • Organizer
      第58回トポロジーシンポジウム
    • Place of Presentation
      筑波大学筑波キャンパス中地区第一エリア1H棟201
    • Year and Date
      2011-08-09
    • Related Report
      2013 Final Research Report
  • [Presentation] Lefschetzファイバー空間の構成と改変について2011

    • Author(s)
      遠藤久顕
    • Organizer
      第58回トポロジーシンポジウム
    • Place of Presentation
      筑波大学(茨城県)(招待講演)
    • Year and Date
      2011-08-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Lefschetzファイバー空間に関するいくつかの話題2011

    • Author(s)
      遠藤久顕
    • Organizer
      Workshop on Lefschetz fibration, broken Lefschetz fibration, and related topics
    • Place of Presentation
      九州大学西新プラザ中会議室
    • Year and Date
      2011-03-29
    • Related Report
      2013 Final Research Report
  • [Presentation] Lantern relations, substitutions, and rational blowdowns of Lefschetz fibrations2010

    • Author(s)
      遠藤久顕
    • Organizer
      Workshop : Category Theory, Computer Science and Topology
    • Place of Presentation
      信州大学理学部講義棟1階・第1講義室
    • Year and Date
      2010-10-17
    • Related Report
      2013 Final Research Report
  • [Presentation] 写像類群の関係式による4次元多様体の改変について2010

    • Author(s)
      遠藤久顕
    • Organizer
      研究集会「リーマン面に関連する位相幾何学」
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-09-05
    • Related Report
      2013 Final Research Report
  • [Presentation] 写像類群の関係式による4次元多様体の改変について2010

    • Author(s)
      遠藤久顕
    • Organizer
      リーヤン面に関連する位相幾何学
    • Place of Presentation
      東京大学大学院数理科学研究科(東京都目黒区)(招待講演)
    • Year and Date
      2010-09-05
    • Related Report
      2010 Annual Research Report
  • [Presentation] Signature of Lefschetz fibrations and related topics2010

    • Author(s)
      Hisaaki Endo
    • Organizer
      Intensive Lectures on Lefschetz fibration
    • Place of Presentation
      Korea Institute of Advanced Study (KIAS), Seoul, Korea
    • Related Report
      2013 Final Research Report
  • [Presentation] Signature of Lefschetz fibrations and related topics2010

    • Author(s)
      Hisaaki Endo
    • Organizer
      Intensive Lectures on Lefschetz Fibration
    • Place of Presentation
      Korea Institute for Advanced Study (韓国・ソウル)
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://t2r2.star.titech.ac.jp/cgi-bin/researcherinfo.cgi?q_researcher_content_number=CTT100380203

    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://www.dma.jim.osaka-u.ac.jp/kg-portal/aspi/RY0011L.asp?UN0=10195&flg=&seq=54766

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://www.dma.jim.osaka-u.ac.jp/kg-portal/aspI/RX0011D.asp?UNO=10195&seq=587

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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