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2011 Fiscal Year Final Research Report

Elucidation of diagrammatic properties of surface-knots and construction of new invariants of surface-knots

Research Project

  • PDF
Project/Area Number 21740042
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo Gakugei University

Principal Investigator

TANAKA Kokoro  東京学芸大学, 教育学部, 講師 (70448950)

Project Period (FY) 2009 – 2011
Keywords位相幾何 / 曲面結び目 / 結び目 / カンドル
Research Abstract

A surface-knot is a closed surface embedded in 4-space, and a diagram of a surface-knots is its projection image into 3-space(whose singularity set is equipped with height information). In this research, we investigate a sheet number of a surface-knot, which is one of its diagramatic properties, by using quandles. Precisely speaking, we show that a sheet number of a 11-colorable 2-knot is at least 7. As an application, we show that spun 6_2 knot has sheet number 7.

  • Research Products

    (12 results)

All 2012 2011 2010 2009 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (10 results) Remarks (1 results)

  • [Journal Article] Complementary regions of knot and link diagrams2011

    • Author(s)
      Colin Adams, Reiko Shinjo, Kokoro Tanaka
    • Journal Title

      Annals of Combinatorics

      Volume: No.4 Pages: 549-563

    • Peer Reviewed
  • [Presentation] 曲面ブレイドのチャート表示とその局所変形について2012

    • Author(s)
      田中心
    • Organizer
      研究集会「Hurwitz Action」
    • Place of Presentation
      大阪市立大学学術情報総合センター文化交流室(大阪府)
    • Year and Date
      20120128-29
  • [Presentation] Interpretation of rack coloring knot invariants in terms of quandles2012

    • Author(s)
      Kokoro Tanaka, Yuma Taniguchi
    • Organizer
      The 8th East Asian School of Knots and Related Topics
    • Place of Presentation
      KAIST, Daejeon(韓国)
    • Year and Date
      20120108-13
  • [Presentation] Khovanov homology for virtual links with two types of maps for Mobius cobordisms2010

    • Author(s)
      Atsushi Ishii, Kokoro Tanaka
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      Colima University, Colima(メキシコ)
    • Year and Date
      20100927-1001
  • [Presentation] カンドル理論の曲面結び目への応用について2010

    • Author(s)
      田中心
    • Organizer
      第57回トポロジーシンポジウム
    • Place of Presentation
      さん太ホール(岡山県)
    • Year and Date
      20100811-14
  • [Presentation] Studies on surface-knots using quandle theory2010

    • Author(s)
      田中心
    • Organizer
      研究集会「4次元トポロジー」
    • Place of Presentation
      広島大学(広島県)
    • Year and Date
      20100118-20
  • [Presentation] 曲面結び目と曲面ブレイドについて2010

    • Author(s)
      田中心
    • Organizer
      早稲田大学教育学部数学教室第98回7階セミナー
    • Place of Presentation
      早稲田大学14号館7階717AB室(東京都)
    • Year and Date
      2010-10-29
  • [Presentation] A recent approach to the smooth 4-dimensional Poincare conjectur2010

    • Author(s)
      田中心
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学数学研究所(大阪府)
    • Year and Date
      2010-02-05
  • [Presentation] Rasmussen不変量とexotic 4-sphereについて:[ Freedman-Gompf-Morrison-Walker, Arxiv : GT. 0906. 5177]の紹介2009

    • Author(s)
      田中心
    • Organizer
      Casson-Freedman理論研究会
    • Place of Presentation
      京都けいはんなプラザホテル(京都府)
    • Year and Date
      20091017-20
  • [Presentation] 曲面結び目や曲面ブレイドに関するいくつかの話題2009

    • Author(s)
      田中心
    • Organizer
      東京女子大学トポロジーセミナー
    • Place of Presentation
      東京女子大学9号館9201教室(東京都)
    • Year and Date
      2009-12-05
  • [Presentation] カンドル理論を用いた曲面結び目の研究に関して2009

    • Author(s)
      田中心
    • Organizer
      信州大学トポロジーセミナー
    • Place of Presentation
      信州大学理学部(長野県)
    • Year and Date
      2009-11-27
  • [Remarks]

    • URL

      http://www.u-gakugei.ac.jp/~kotanaka/

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Published: 2013-07-31  

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