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4-MANIFOLDS AND RIEMANN SURFACES

Research Project

Project/Area Number 20340014
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

MATSUMOTO Yukio  学習院大学, 理学部, 教授 (20011637)

Co-Investigator(Kenkyū-buntansha) ASHIKAGA Tadashi  東北学院大学, 工学部, 教授 (90125203)
Co-Investigator(Renkei-kenkyūsha) KAMADA Seiichi  広島大学, 理学系研究科, 教授 (60254380)
KAWAZUMI Nariya  東京大学, 数理科学研究科, 准教授 (30214646)
ENDO Hisaaki  東京工業大学, 理工学研究科, 教授 (20323777)
YOSHIKAWA Ken-ichi  京都大学, 理学研究科, 教授 (20242810)
TAKAMURA Shigeru  京都大学, 理学研究科, 准教授 (20362436)
IWASE Zjunici  金沢大学, 自然科学研究科, 助教 (70183746)
Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥12,740,000 (Direct Cost: ¥9,800,000、Indirect Cost: ¥2,940,000)
Fiscal Year 2011: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
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: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Keywords位相幾何学 / 4次元多様体 / リーマン面 / モジュライ空間 / コンパクト化 / オービフォールド / 局所符号数 / グルポイド / 普遍退化族 / 特異ファイバーの分裂 / 符号数 / タイヒミュラー空間 / 写像類群
Research Abstract

A Riemann surface is a closed surface carrying a complex structure. The isomorphism classes of Riemann surfaces make a complex orbifold called the moduli space. It can be compactified by adding certain "boundaries". The main achievement is that we have succeeded in constructing a "universal degenerating family of Riemann surfaces" over the compactified moduli space. A paper is now in preparation, but the result is expected to be applied in many problems of 4-manifolds which are fibered by Riemann surfaces.

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

    (63 results)

All 2012 2011 2010 2009 2008 Other

All Journal Article (23 results) (of which Peer Reviewed: 7 results) Presentation (37 results) Book (3 results)

  • [Journal Article] Bridge presentations of virtual knots2011

    • Author(s)
      M. Hirasawa, N. Kamada and S. Kamada
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 20 Issue: 06 Pages: 881-893

    • DOI

      10.1142/s0218216511009017

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

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

      J. of Topology

      Volume: 4 Pages: 227-253

    • Related Report
      2011 Final Research Report
  • [Journal Article] On the Universal Degenerating Family of Riemann Surfaces2011

    • Author(s)
      Yukio Matsumoto
    • Journal Title

      Proceedings of the Franco-Japanese Singularity Symposium

      Volume: (受理 (近刊))

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local signature defect of fibered complex surfaces via moduli and monodromy2010

    • Author(s)
      T. Ashikaga
    • Journal Title

      Demonstratio Math. XLIII

      Pages: 263-279

    • Related Report
      2011 Final Research Report
  • [Journal Article] Local signature defect of fibered complex surfaces via monodromy and stable reduction2010

    • Author(s)
      T. Ashikaga
    • Journal Title

      Comment. Math. Helv

      Volume: 85 Pages: 417-461

    • Related Report
      2011 Final Research Report
  • [Journal Article] New invariants of long virtual knots2010

    • Author(s)
      A. Bartholomew, R. Fenn, N. Kamada and S. Kamada
    • Journal Title

      Kobe J. Math

      Volume: 27 Pages: 21-33

    • Related Report
      2011 Final Research Report
  • [Journal Article] Homology groups of symmetric quandles and cocycle invariants of links and surface-links2010

    • Author(s)
      S. Kamada and K. Oshiro
    • Journal Title

      Trans. Amer. Math. Soc

      Volume: 362 Pages: 5501-5527

    • Related Report
      2011 Final Research Report
  • [Journal Article] Lantern relations and rational blowdowns2010

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

      Proc. of Amer. Math. Soc

      Volume: 138 Pages: 1131-1142

    • Related Report
      2011 Final Research Report
  • [Journal Article] Local signature defect of fibered complex surfaces via monodromy and stable reduction2010

    • Author(s)
      T.Ashikaga
    • Journal Title

      Comment.Math.Helv. 85

      Pages: 417-461

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Local signature defect of fibered complex surfaces via monodromy and stable reduction2010

    • Author(s)
      T.Ashikaga
    • Journal Title

      Comment.Math.Hely. 85

      Pages: 417-461

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A divisor on the moduli spaces of curves assorciated to the signature of fibered complex surfaces(with appendix by Kazuhiro Konno)2009

    • Author(s)
      T. Ashikaga and K.-I. Yoshikawa
    • Journal Title

      Adv. St. Pure Math

      Volume: 56 Pages: 1-34

    • Related Report
      2011 Final Research Report
  • [Journal Article] Canonical lifts of the Johnson homomorphisms to the Torelli groupoid2009

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

      Adv. Math.

      Volume: 221 Pages: 627-659

    • Related Report
      2011 Final Research Report
  • [Journal Article] Calabi-Yau threefolds of Borcera-Voisin, analytic torsion, and Borcherds products2009

    • Author(s)
      K.-I. Yoshikawa
    • Journal Title

      Asterisque

      Volume: 328 Pages: 355-393

    • Related Report
      2011 Final Research Report
  • [Journal Article] Canonical 2-forms on the moduli space of Riemann surfaces,"Handbook of Teichmuller theory" ed. by A. Papadopoulos, II2009

    • Author(s)
      N. Kawazumi
    • Journal Title

      EMS Publishing House, Zurich

      Pages: 217-237

    • Related Report
      2011 Final Research Report
  • [Journal Article] A divisor on the moduli space of curves associated to the signature of fibered complex surfaces(with an Appendix by Kazuhiro Konno)2009

    • Author(s)
      T.Ashikaga, K.Yoshikawa
    • Journal Title

      Advanced St.Pure Math. 56

      Pages: 1-34

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

    • Author(s)
      N. Kawazumi
    • Journal Title

      Geometry & Topology Monographs

      Volume: 13 Pages: 293-306

    • Related Report
      2011 Final Research Report
  • [Journal Article] The virtual magnetic Kauffman bracket skein module and skein relations for the f-polynomial2008

    • Author(s)
      A. Ishii, N. Kamada and S. Kamada
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 17 Pages: 675-688

    • Related Report
      2011 Final Research Report
  • [Journal Article] Analytic torsion for Calabi-Yau threefolds2008

    • Author(s)
      H. Fang, Z. Lu and K.-I. Yoshikawa
    • Journal Title

      J. Diff. Geom

      Volume: 80 Pages: 175-259

    • Related Report
      2011 Final Research Report
  • [Journal Article] On the universal degenerating family of Riemann surfaces

    • Author(s)
      Y. Matsumoto
    • Journal Title

      Proceedings of the 5-th Franco-Japanese Singularity Symposium

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
  • [Journal Article] The center of the Goldman Lie algebra of a surface of infinite genus

    • Author(s)
      N. Kawazumi and Y. Kuno
    • Journal Title

      Quartery J. of Mathematics

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
  • [Journal Article] K3 surfaces with involution, equivariant analytic torsion, and automorphic forms on the moduli space II

    • Author(s)
      K.-I. Yoshikawa
    • Journal Title

      Journal fur die reine und angewandte Matematik

      Volume: (to appear)

    • Related Report
      2011 Final Research Report
  • [Journal Article] On the Universal Degenerating family of Riemann surfaces

    • Author(s)
      Y.Matsumoto
    • Journal Title

      Accepted by IRMA series(Strasbourg)

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Pseudo-Periodic maps and Degeneration of Riemann Surfaces

    • Author(s)
      Y.Matsumoto, J.M.Montesinos
    • Journal Title

      accepted by Lecture Notes in Mathematics, Springer-Verlag

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Presentation] Extended Zagier reciprocity for Dedekind sum via cyclic quotient singularities2012

    • Author(s)
      足利正
    • Organizer
      Topology of Singularities and Related Topics III
    • Place of Presentation
      Dalat Vietnam
    • Year and Date
      2012-03-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Extended Zagier reciprocity for Dedekind sum via cyclic quotient singularities2012

    • Author(s)
      足利正
    • Organizer
      Topology and Singularities and Related Topics III
    • Place of Presentation
      Dalat, Vietnam(招待講演)
    • Year and Date
      2012-03-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Dedekind和に関するZagier相互律の拡張と巡回商特異点間の双対性2012

    • Author(s)
      足利正
    • Organizer
      代数幾何ミニワークショップ
    • Place of Presentation
      兵庫県多可町
    • Year and Date
      2012-02-11
    • Related Report
      2011 Final Research Report
  • [Presentation] 特異点に関する高次元連分数とZagier相互律2011

    • Author(s)
      足利正
    • Organizer
      リーマン面に関する位相幾何学研究集会
    • Place of Presentation
      東京大学
    • Year and Date
      2011-09-04
    • Related Report
      2011 Final Research Report
  • [Presentation] タイヒミュラー・モジュライ空間のコンパクト化とその上の普遍退化族について2011

    • Author(s)
      松本幸夫
    • Organizer
      Mejiro mini-workshop on geometry and topology
    • Place of Presentation
      学習院大学
    • Year and Date
      2011-05-28
    • Related Report
      2011 Final Research Report
  • [Presentation] タイヒミュラー・モジュライ空間のコンパクト化とその上の普遍退化族について2011

    • Author(s)
      松本幸夫
    • Organizer
      Mejiro mini-workshop on geometry and topology
    • Place of Presentation
      学習院大学(招待講演)
    • Year and Date
      2011-05-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Axial fibrations of the Fermat surfaces and their singular fibers(with Kazuo Masuda)2011

    • Author(s)
      松本幸夫
    • Organizer
      IRMAセミナー
    • Place of Presentation
      Univ. Strasbourg
    • Year and Date
      2011-02-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Determination of singular fibers in the Fermat surfaces2011

    • Author(s)
      Y.Matsumoto
    • Organizer
      Geometry and Topology Seminar, IRMA
    • Place of Presentation
      Strasbourg Univ.
    • Year and Date
      2011-02-28
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Determination of singular fibers in the Fermat surfaces2011

    • Author(s)
      Yukio Matsumoto
    • Organizer
      Geometry and Topology Seminar, IRMA, Strasbourg University
    • Place of Presentation
      ストラスブール大学(招待講演)
    • Year and Date
      2011-02-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] Low dimensional topology and complex analysis2011

    • Author(s)
      松本幸夫
    • Organizer
      The 7-th East Asian School of Knots and Related Topics
    • Place of Presentation
      広島大学
    • Year and Date
      2011-01-11
    • Related Report
      2011 Final Research Report
  • [Presentation] On the universal orbifold family of Riemann surfaces over the compactified moduli space2011

    • Author(s)
      松本幸夫
    • Organizer
      「リーマン面・不連続群論」研究集会
    • Place of Presentation
      大阪国際交流センター
    • Year and Date
      2011-01-08
    • Related Report
      2011 Final Research Report
  • [Presentation] On the universal orbifold family of Riemann surfaces over the compactified moduli space2011

    • Author(s)
      Y.Matsumoto
    • Organizer
      「リーマン面・不連続群」研究集会
    • Place of Presentation
      大阪国際交流センター
    • Year and Date
      2011-01-08
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On the universal orbifold family of Riemann surfaces over the Compactified moduli space2011

    • Author(s)
      Yukio Matsumoto
    • Organizer
      「リーマン面・不連続群」研究集会
    • Place of Presentation
      大阪国際交流センター(招待講演)
    • Year and Date
      2011-01-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 巡回商特異点に関する高次連分数とZagier相互律2011

    • Author(s)
      足利正
    • Organizer
      リーマン面に関する位相幾何学研究集会
    • Place of Presentation
      東京大学(招待講演)
    • Related Report
      2011 Annual Research Report
  • [Presentation] Low dimensional topology and complex analysis2011

    • Author(s)
      Y.Matsumoto
    • Organizer
      The 7-th East Asian School of Knots and Related Topics
    • Place of Presentation
      Hiroshima Univ.
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] Low dimensional topology and complex analysis2011

    • Author(s)
      Yukio Matsumoto
    • Organizer
      The 7^<th> East Asian School of Knots and Realted Topics
    • Place of Presentation
      広島大学(招待講演)
    • Related Report
      2010 Annual Research Report
  • [Presentation] Planer continued linear fraction for 3-dimensional cyclic quotient singularities2010

    • Author(s)
      足利正
    • Organizer
      第二回東北復旦代数幾何交流シンポジューム
    • Place of Presentation
      複旦大学
    • Year and Date
      2010-06-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Toric resolution of a certain non-normal singularity2010

    • Author(s)
      Y.Matsumoto
    • Organizer
      山形特異点セミナー
    • Place of Presentation
      山形大学
    • Related Report
      2010 Self-evaluation Report 2009 Annual Research Report
  • [Presentation] Towards resolution of surface singularity via toroidal fiber space2010

    • Author(s)
      足利正
    • Organizer
      代数幾何ミニワークショップ
    • Place of Presentation
      兵庫県八千代町
    • Related Report
      2009 Annual Research Report
  • [Presentation] Towards the signature of complex surfaces and singularities2010

    • Author(s)
      足利正
    • Organizer
      Mini Workshop on Singularity Theory
    • Place of Presentation
      東京理科大学
    • Related Report
      2009 Annual Research Report
  • [Presentation] Another geometric proof of the reciprocity law of Dedekind sum(jointly with M. Ishizaka)2009

    • Author(s)
      足利正
    • Organizer
      第一回東北復旦代数幾何交流シンポジューム
    • Place of Presentation
      東北大学
    • Year and Date
      2009-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Signature divisor on moduli space of curves and its application2009

    • Author(s)
      足利正
    • Organizer
      The 5-th Franco-Japanese singularity symposium
    • Place of Presentation
      Univ. Strasbourg
    • Year and Date
      2009-08-27
    • Related Report
      2011 Final Research Report
  • [Presentation] On the universal degenerating family of Riemann surfaces over the compactified moduli space2009

    • Author(s)
      松本幸夫
    • Organizer
      The 5-th Franco-Japanese singularity symposium
    • Place of Presentation
      Univ. Strasbourg
    • Year and Date
      2009-08-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Local signature and eta invariant of degeneration Of Riemann surfaces2009

    • Author(s)
      足利 正
    • Organizer
      Branched Coverings, Degenerations, and Related Topics
    • Place of Presentation
      広島大学理学部
    • Year and Date
      2009-03-12
    • Related Report
      2008 Annual Research Report
  • [Presentation] Degeneration of pointed spheres (A topological interpretation)2009

    • Author(s)
      松本 幸夫
    • Organizer
      Branched Coverings, Degenerations, and Related Topics
    • Place of Presentation
      広島大学理学部
    • Year and Date
      2009-03-09
    • Related Report
      2008 Annual Research Report
  • [Presentation] 曲線の退化ファイバー芽のエータ不変量に関する-考察2009

    • Author(s)
      足利 正
    • Organizer
      代数幾何学ミニワークショップ
    • Place of Presentation
      兵庫県八千代市
    • Year and Date
      2009-02-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Signature Divisor on the moduli space of curves and Its applications2009

    • Author(s)
      足利 正
    • Organizer
      第4回代数・幾何・解析セミナー
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2009-02-17
    • Related Report
      2008 Annual Research Report
  • [Presentation] Another geometric proof of the reciprocity law of Dedekind sum (jointly with M.Ishizaka)2009

    • Author(s)
      Y.Matsumoto
    • Organizer
      第1回東北復旦代数幾何交流シンポジューム
    • Place of Presentation
      東北大学
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] On local signature and Horikawa index of fibered surfaces2009

    • Author(s)
      足利正
    • Organizer
      Hodge理論と代数幾何学
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2009 Annual Research Report
  • [Presentation] Local signature of fibered surface and its application2009

    • Author(s)
      足利正
    • Organizer
      Conference on Algebraic surfaces and related topics
    • Place of Presentation
      Pohang, 韓国
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the universal degenerating family of Riemann surfaces2009

    • Author(s)
      松本幸夫
    • Organizer
      Franco-Japan symposium on Singularity
    • Place of Presentation
      Strasbourg, フランス
    • Related Report
      2009 Annual Research Report
  • [Presentation] Signature divisor on moduli space of curves and its application2009

    • Author(s)
      足利正
    • Organizer
      Franco-Japan symposium on Singularity
    • Place of Presentation
      Strasbourg, フランス
    • Related Report
      2009 Annual Research Report
  • [Presentation] Localization of signature of fibered complex surfaces2009

    • Author(s)
      足利正
    • Organizer
      2009年度代数幾何学シンポジューム
    • Place of Presentation
      兵庫県城崎大会議館
    • Related Report
      2009 Annual Research Report
  • [Presentation] Another geometric proof of the reciprocity of Dedekind sum(jointly with M.Ishizaka)2009

    • Author(s)
      足利正
    • Organizer
      第一回東北復旦代数幾何交流シンポジューム
    • Place of Presentation
      東北大学
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the universal degenerating family of Riemann surfaces2008

    • Author(s)
      松本幸夫
    • Organizer
      Geometry of singularities and manifolds
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2008-09-16
    • Related Report
      2011 Final Research Report
  • [Presentation] On the universal degenerating famly of Riemann surfaces2008

    • Author(s)
      松本 幸夫
    • Organizer
      特異点と多様体の幾何-草津2008-
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2008-09-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] Localization of the signature of fibered complex surfaces2008

    • Author(s)
      足利 正
    • Organizer
      International Conference on finite And infinite dimensional complex analysis
    • Place of Presentation
      韓国、Gyengju大学
    • Year and Date
      2008-07-28
    • Related Report
      2008 Annual Research Report
  • [Book] 曲面結び目理論2012

    • Author(s)
      鎌田聖一
    • Total Pages
      247
    • Publisher
      丸善出版
    • Related Report
      2011 Final Research Report
  • [Book] Pseudo-periodic maps and degeneration of Riemann surfaces2011

    • Author(s)
      松本幸夫・Jose Maria Montesinos-Amilibia
    • Total Pages
      235
    • Publisher
      Springer-Verlag
    • Related Report
      2011 Final Research Report
  • [Book] Pseudo-periodic maps and degeneration of Riemann surfaces2011

    • Author(s)
      Y.Matsumoto, J.M.Montesinos-Amilibia
    • Total Pages
      235
    • Publisher
      Springer-Verlag
    • Related Report
      2011 Annual Research Report

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

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