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A Study on the faithfulness of the graded Magnus representation of the mapping class group

Research Project

Project/Area Number 21740033
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionAkita University

Principal Investigator

SUZUKI Masaaki  秋田大学, 教育文化学部, 准教授 (70431616)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords写像類群 / 線型表現
Research Abstract

In order to consider the faithfulness of the graded Magnus representation of the mapping class group, we obtained some elements which belong to the kernel of the Magnus representation of the Torelli group, which is the first case of the graded Magnus representation of the mapping class group. Further we showed that these elements do not belong to the second Magnus representation of the mapping class group.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (17 results)

All 2012 2011 2010 2009 Other

All Journal Article (6 results) (of which Peer Reviewed: 3 results) Presentation (11 results)

  • [Journal Article] An epimorphism between knot groups which does not map a meridian to a meridian II2012

    • Author(s)
      Masaaki Suzuki
    • Journal Title

      群の表現及び表現空間の幾何学的・解析的研究数理解析研究所講究録

      Volume: 1777 Pages: 103-106

    • Related Report
      2011 Annual Research Report
  • [Journal Article] An epimorphism between knot groups which does not map a meridian to a meridian2011

    • Author(s)
      Masaaki Suzuki
    • Journal Title

      Twisted topological invariants and topology of lowdimensional manifolds数理解析研究所講究録

      Volume: 1747 Pages: 135-139

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Representations of the braid group and punctured torus bundles2009

    • Author(s)
      T.Morifuji, M.Suzuki
    • Journal Title

      Kyungpook Mathematical Journal 49

      Pages: 7-14

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An epimorphism between knot groups which does not map a meridian to a meridian

    • Author(s)
      Masaki Suzuki
    • Journal Title

      数理解析研究所講究録1747 Twisted topological invariants and topology of low-dimensional manifolds

      Pages: 135-139

    • Related Report
      2011 Final Research Report
  • [Journal Article] A partial order on the set of prim knots with up to 11 crossings

    • Author(s)
      Keiichi Horie, Teruaki Kitano, Mineko Matsumoto and Masaaki Suzuki
    • Journal Title

      Journal of Knot Theory and its Ramifications

      Volume: Volume 20 Pages: 275-303

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Representations of the braid group and punctured torus bundles

    • Author(s)
      Takayuki Morifuji and Masaaki Suzuki
    • Journal Title

      Kyungpook Mathematical Journal

      Volume: Volume 49 Pages: 7-14

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Presentation] Epimorphism between knot groups and the images of meridians2011

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Circle valued Morse theory and Alexander invariants
    • Place of Presentation
      東京大学
    • Year and Date
      2011-11-17
    • Related Report
      2011 Final Research Report
  • [Presentation] メリディアンを保たない結び目群間の全射について2011

    • Author(s)
      鈴木正明
    • Organizer
      トポロジーとコンピュータ2011
    • Place of Presentation
      名城大学
    • Year and Date
      2011-11-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphism between knot groups and the images of meridians2011

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology Seminar
    • Place of Presentation
      北京大学
    • Year and Date
      2011-10-12
    • Related Report
      2011 Final Research Report
  • [Presentation] 自由結合代数の微分のなすリー代数のアーベル化2011

    • Author(s)
      森田茂之, 逆井卓也, 鈴木正明
    • Organizer
      リーマン面に関連する位相幾何学
    • Place of Presentation
      東京大学
    • Year and Date
      2011-09-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphisms between knot groups : determination of the partial order2010

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Twisted topological invariants and topology of low dimensional manifolds
    • Place of Presentation
      あきた白神体験センター
    • Year and Date
      2010-09-14
    • Related Report
      2011 Final Research Report
  • [Presentation] On the graded Magnus representation of the mapping class group2010

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology and Computer2010
    • Place of Presentation
      東京工業大学
    • Year and Date
      2010-09-10
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphisms between knot groups2010

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Claremont Topology Seminar
    • Place of Presentation
      ピッツァー大学
    • Year and Date
      2010-03-02
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphisms between knot groups2009

    • Author(s)
      Masaaki Suzuki
    • Organizer
      CalTech Geometry and Topology Seminar
    • Place of Presentation
      カリフォルニア工科大学
    • Year and Date
      2009-12-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphisms between knot groups2009

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Geometry and Topology Seminar
    • Place of Presentation
      南カリフォルニア大学
    • Year and Date
      2009-10-12
    • Related Report
      2011 Final Research Report
  • [Presentation] Epimorphisms between knot groups of 2-bridge knots with up to 12 crossings2009

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology and Computer 2009
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-09-01
    • Related Report
      2011 Final Research Report
  • [Presentation] A partial order on the set of prime knots with up to 11 crossings2009

    • Author(s)
      Masaaki Suzuki
    • Organizer
      Topology Seminar
    • Place of Presentation
      トゥールーズ大学
    • Year and Date
      2009-06-10
    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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