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

2011 Fiscal Year Final Research Report

• Project/Area Number: 21740033
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Akita University
• Principal Investigator: SUZUKI Masaaki 秋田大学, 教育文化学部, 准教授 (70431616)
• Project Period (FY): 2009 – 2011
• 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.

Research Products

• [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
• [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
  • 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
  • Peer Reviewed
• [Presentation] Epimorphism between knot groups and the images of meridians (2011)
  • 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
• [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
• [Presentation] Epimorphism between knot groups and the images of meridians (2011)
  • Author(s): Masaaki Suzuki
  • Organizer: Topology Seminar
  • Place of Presentation: 北京大学
  • Year and Date: 2011-10-12
• [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
• [Presentation] Epimorphisms between knot groups : determination of the partial order (2010)
  • 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
• [Presentation] On the graded Magnus representation of the mapping class group (2010)
  • Author(s): Masaaki Suzuki
  • Organizer: Topology and Computer2010
  • Place of Presentation: 東京工業大学
  • Year and Date: 2010-09-10
• [Presentation] Epimorphisms between knot groups (2010)
  • Author(s): Masaaki Suzuki
  • Organizer: Claremont Topology Seminar
  • Place of Presentation: ピッツァー大学
  • Year and Date: 2010-03-02
• [Presentation] Epimorphisms between knot groups (2009)
  • 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
• [Presentation] Epimorphisms between knot groups (2009)
  • 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
• [Presentation] Epimorphisms between knot groups of 2-bridge knots with up to 12 crossings (2009)
  • Author(s): Masaaki Suzuki
  • Organizer: Topology and Computer 2009
  • Place of Presentation: 東京工業大学
  • Year and Date: 2009-09-01
• [Presentation] A partial order on the set of prime knots with up to 11 crossings (2009)
  • Author(s): Masaaki Suzuki
  • Organizer: Topology Seminar
  • Place of Presentation: トゥールーズ大学
  • Year and Date: 2009-06-10