• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Topological Studies around Riemann Surfaces

Research Project

Project/Area Number 18204002
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

KAWAZUMI Nariya  The University of Tokyo, 大学院・数理科学研究科, 准教授 (30214646)

Co-Investigator(Kenkyū-buntansha) MATSUMOTO Yukio  学習院大学, 理学部, 教授 (20011637)
MORITA Shigeyuki  東京大学, 大学院・数理科学研究科, 名誉教授 (70011674)
HASHIMOTO Yoshitake  東京都市大学, 知識工学部, 教授 (20271182)
SHIBUKAWA Youichi  北海道大学, 大学院・理学研究院, 准教授 (90241299)
AKITA Toshiyuki  北海道大学, 大学院・理学研究院, 准教授 (30279252)
ENDO Hisaaki  大阪大学, 大学院・理学研究科, 准教授 (20323777)
ASUKE Taro  東京大学, 大学院・数理科学研究科, 准教授 (30294515)
TADOKORO Yuuki  木更津工業高等専門学校, 基礎学系, 准教授 (10435414)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥32,760,000 (Direct Cost: ¥25,200,000、Indirect Cost: ¥7,560,000)
Fiscal Year 2009: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2008: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2007: ¥7,930,000 (Direct Cost: ¥6,100,000、Indirect Cost: ¥1,830,000)
Fiscal Year 2006: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
Keywordsリーマン面 / 写像類群 / モジュライ空間 / マグナス展開 / アラケロフ・グリーン函数 / ゴールドマン・リー代数 / 非可換ピカール・レフシェッツ公式 / デーン・ツイスト / ピカール・レフシェッツ公式 / 形式的シンプレクティック幾何 / ストリング・トポロジー / 位相幾何学 / 森田マンフォード類 / ジョンソン準同型 / 複素解析葉層 / ゲルファント・フクス・コホモロジー / ファットグラフ / 複素解析的ベクトル場 / 複素解析ベクトル場
Research Abstract

Bene, Penner and the principal investigator discovered fatgraph Magnus expansions, which connects a combinatorial structure of a Riemann surface directly to some algebraic aspects of the mapping class groups. The principal investigator also discovered a new analytic invariant of a closed Riemann surface to describe how curved the moduli space of Riemann surfaces is. Kuno and the principal investigator discovered a new connection between two refinements of the intersection form on a Riemann surfaces, the Goldman Lie algebras and the Lie algebras of symplectic derivations. As an application, they proved a non-commutative analogue of the Picard-Lefschetz formula.

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (44 results)

All 2011 2010 2009 2008 2007 2006

All Journal Article (22 results) (of which Peer Reviewed: 11 results) Presentation (22 results)

  • [Journal Article] Canonical 2-forms on the moduli space of Riemann surfaces2009

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Handbook of Teichmueller theory(edited by A.Papadopoulos, Volume II, EMS Publishing House, Zurich)

      Pages: 217-237

    • Related Report
      2009 Final Research Report
  • [Journal Article] Canonical lifts of the Johnson homomorphisms to the Torelli groupoid2009

    • Author(s)
      Alex Bene, Nariya Kawazumi, Robert Penner
    • Journal Title

      Adv.Math. 221

      Pages: 627-659

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Canonical 2-forms on the moduli space of Riemann surfaces2009

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Handbook of Teichmueller theory

      Volume: 2 Pages: 217-237

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Canonical lifts of the Johnson homomorphisms to the Torelli groupoid2009

    • Author(s)
      A. J. Bene, N. Kawazumi and R. C.Penner
    • Journal Title

      Advances in Mathematics vol.221

      Pages: 627-659

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Canonical 2-forms on the moduli space of Riemann surfaces2009

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Handbook of Teichmuller theory. 2

      Pages: 217-237

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Canonical extensions of the Johnson homomorphisms to the Torelli groupoid2009

    • Author(s)
      A.J.Bene, N.Kawazumi, R.C.Pen
    • Journal Title

      Advances in Mathematics 221

      Pages: 627-659

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the stable cohomology algebra of extended mapping class groups for surfaces2008

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Advanced Studies in Pure Mathematics (Groups of Diffeomorphisms) 52

      Pages: 383-400

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

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

      Math.Proc.Camb.Phil.Soc. 144

      Pages: 411-421

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Twisted Morita-Mumford classes on braid groups2008

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Geometry & Topology Monographs 13

      Pages: 293-306

    • Related Report
      2009 Final Research Report 2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the stable cohomology algebra of extended mapping class groups for surfaces2008

    • Author(s)
      N. Kawazumi
    • Journal Title

      Advanced Studies in Pure Mathematics vol.52

      Pages: 383-400

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

    • Author(s)
      T. Akita and N. Kawazumi
    • Journal Title

      Math. Proc. Camb. Phil. Soc. vol.144

      Pages: 411-421

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Twisted Morita-Mumford classes on braid groups2008

    • Author(s)
      N. Kawazumi
    • Journal Title

      Geometry and Topology Monographseries vol.13

      Pages: 293-306

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the stable cohomology algebra of extended mapping class groups for surfaces2008

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Adv.Stud.Pure Math. 52

      Pages: 383-400

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Integral Riemann-Roch formulae for cyclic subgroups of mapping class groups2008

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

      Math.Proc.Camb.Phil.Soc 14

      Pages: 411-421

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characteristic classes of foliated surface bundles with a rea-preserving holonomy2007

    • Author(s)
      D.Kotschick, S.Morita
    • Journal Title

      Journal of Differential Geometry 75

      Pages: 273-302

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Oberwolfach Reports 3-2

      Pages: 1555-1557

    • Related Report
      2009 Final Research Report
  • [Journal Article] Harmonic Magnus Expansion on the Universal Family of Riemann Survaces2006

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Oberwolfach Reports 3-1

      Pages: 770-772

    • Related Report
      2009 Final Research Report
  • [Journal Article] Harmonic Magnus Expansion on the Universal Family of Riemann Survaces2006

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Oberwolfach Reports 3・1

      Pages: 770-772

    • Related Report
      2006 Annual Research Report
  • [Journal Article] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      Nariya Kawazumi
    • Journal Title

      Oberwolfach Reports 3・2

      Pages: 1555-1557

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Cohomological structure of the mapping class group and beyond2006

    • Author(s)
      Shigeyuki Morita
    • Journal Title

      Proc. Sympos. Pure Math. "Problems on Mapping Class Groups and Related Topics" 74

      Pages: 329-354

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Various aspects of degenerate families of Riemann surfaces2006

    • Author(s)
      T.Ashikaga, H.Endo
    • Journal Title

      Sugaku Expositions 19

      Pages: 171-196

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On infinitesimal derivatives of the Bott class2006

    • Author(s)
      Taro Asuke
    • Journal Title

      in : 'Foliation 2005', World Scientific, Singapore

      Pages: 37-46

    • Related Report
      2006 Annual Research Report
  • [Presentation] The logarithms of Dehn twists2011

    • Author(s)
      河澄響矢
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2011
    • Place of Presentation
      首都大学東京 南大沢キャンパス
    • Year and Date
      2011-03-10
    • Related Report
      2009 Final Research Report
  • [Presentation] The logarithms of Dehn twists2011

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「Branched Coverings, Degenerations, and Related Topics-2011」
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach(ドイツ)
    • Year and Date
      2011-03-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the Turaev cobracket on the Lie algebra of symplectic derivations2011

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM (Center for Quantum Geometry of Moduli Spaces)
    • Place of Presentation
      University of Aarhus (デンマーク)
    • Year and Date
      2011-01-26
    • Related Report
      2009 Final Research Report
  • [Presentation] On the Turaev cobracket on the Lie algebra of symplectic derivations2011

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM (Center for Quantum Geometry of Moduli Spaces)
    • Place of Presentation
      University of Aarhus(デンマーク)
    • Year and Date
      2011-01-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] The Chas-Sullivan conjecture for a surface of infinite genus2010

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「トポロジーの現在と未来」
    • Place of Presentation
      文部科学省共済組合箱根宿泊所
    • Year and Date
      2010-12-21
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      河澄響矢
    • Organizer
      大阪大学大学院理学研究科数学教室談話会
    • Place of Presentation
      大阪大学大学院理学研究科数学専攻
    • Year and Date
      2010-12-13
    • Related Report
      2009 Final Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Workshop 'Teichmueller Theory,'
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach.(ドイツ)
    • Year and Date
      2010-12-13
    • Related Report
      2009 Final Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      河澄響矢
    • Organizer
      大阪大学数学教室談話会
    • Place of Presentation
      大阪大学大学院理学研究科
    • Year and Date
      2010-12-13
    • Related Report
      2009 Annual Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Workshop 'Teichmueller Theory'
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach(ドイツ)
    • Year and Date
      2010-12-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] The Goldman Lie algebra and Kontsevich's associative symplectic geometry2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM (Center for Quantum Geometry of Moduli Spaces)
    • Place of Presentation
      University of Aarhus (デンマーク)
    • Year and Date
      2010-09-28
    • Related Report
      2009 Final Research Report
  • [Presentation] The Goldman Lie algebra and Kontsevich's associative symplectic geometry2010

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Seminar at QGM (Center for Quantum Geometry of Moduli Spaces)
    • Place of Presentation
      University of Aarhus(デンマーク)
    • Year and Date
      2010-09-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      久野雄介、河澄響矢
    • Organizer
      日本数学会秋季分科会一般講演
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2009 Final Research Report
  • [Presentation] The logarithms of Dehn twists2010

    • Author(s)
      久野雄介、河澄響矢
    • Organizer
      日本数学会秋季分科会
    • Place of Presentation
      名古屋大学(一般講演)
    • Year and Date
      2010-09-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Johnson's homomorphisms and the Arakelov-Green function2007

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「離散群と双曲空間の解析学とトポロジー」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-12
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Johnson's homomorphisms and the Arakelov-Green function2007

    • Author(s)
      河澄 響矢
    • Organizer
      離散群と双曲空間の解析学とトポロジー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-12-12
    • Related Report
      2007 Annual Research Report
  • [Presentation] 実および複素一次元のゲルファントフクスコホモロジー2007

    • Author(s)
      河澄響矢
    • Organizer
      研究集会「複素微分方程式の定性的理論と関連する幾何」
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2007-06-29
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Topology Seminar, CTQM
    • Place of Presentation
      University of Aarhus(デンマーク)
    • Year and Date
      2006-11-07
    • Related Report
      2009 Final Research Report
  • [Presentation] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      河澄響矢
    • Organizer
      Workshop 'Groups of Diffeomorphisms 2006,'
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2006-09-11
    • Related Report
      2009 Final Research Report
  • [Presentation] 第一森田マンフォード類を表すいろいろな微分形式について2006

    • Author(s)
      河澄響矢
    • Organizer
      第3回トポロジー・代数幾何蔵王セミナー
    • Place of Presentation
      蔵王ハイツ
    • Year and Date
      2006-07-27
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      Nariya Kawazumi
    • Organizer
      Workshop 'Teichmuller Space (Classical and Quantum),'
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach.(ドイツ)
    • Year and Date
      2006-05-30
    • Related Report
      2009 Final Research Report
  • [Presentation] A higher analogue of the period matrix of a compact Riemann surface2006

    • Author(s)
      河澄響矢
    • Organizer
      Topology Seminar, CTQM
    • Place of Presentation
      University of Aarhus
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] A higher analogue of the period matrix of a compact Riemann surface, Workshop2006

    • Author(s)
      河澄響矢
    • Organizer
      Groups of Diffeomorphisms2006
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2008 Self-evaluation Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi