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Study on topological properties of quantum invariants concerning to knot cobordism

Research Project

Project/Area Number 23740046
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionGifu University

Principal Investigator

TANAKA Toshifumi  岐阜大学, 教育学部, 准教授 (60396851)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords結び目コボルディズム / 量子不変量 / 対称和 / 微分構造 / スライス結び目 / リボン結び目 / 結び目 / 国際情報交換(韓国) / 国際情報交流(韓国)
Research Abstract

In a mathematical investigation of knots, some studies for a classification of a knot and its application were done by using algebraic and topological methods. As a result, a relationship between given two knots has been investigated by using items called quantum invariants. As applications to the study of smooth structures of non-compact 4-manifolds (Casson handles, the connected sum of complex projective planes), and to the study of spatial graphs via contact geometry, some results concerning to the classifications have been obtained.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (19 results)

All 2014 2013 2012 2011

All Journal Article (8 results) (of which Peer Reviewed: 2 results) Presentation (11 results)

  • [Journal Article] Signed Gordian distances, the Jones polynomial and Rasmussen invariant of knots2014

    • Author(s)
      Tanaka, Toshifumi
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 第38巻 Pages: 5-14

    • NAID

      110009864345

    • Related Report
      2013 Final Research Report
  • [Journal Article] Signed Gordian distances, the Jones polynomial and Rasmussen invariant of knots2014

    • Author(s)
      Tanaka, Toshifumi
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 38 Pages: 5-14

    • NAID

      110009864345

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Positive knots and Rasmussen's invariant2013

    • Author(s)
      Tanaka, Toshifumi
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 第37巻 Pages: 1-5

    • NAID

      110009559095

    • Related Report
      2013 Final Research Report
  • [Journal Article] Positive knots and Rasmussen's invariant2013

    • Author(s)
      田中利史
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 37 Pages: 1-5

    • NAID

      110009559095

    • Related Report
      2012 Research-status Report
  • [Journal Article] An infinite family of prime satellite knots with the same Alexander polynomial2012

    • Author(s)
      Tanaka, Toshifumi
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 第36巻 Pages: 1-4

    • NAID

      110009422749

    • Related Report
      2013 Final Research Report
  • [Journal Article] AN INFINITE FAMILY OF CASSON HANDLES AND THE RASMUSSEN INVARIANT OF A KNOT2011

    • Author(s)
      Tanaka, Toshifumi
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 20, no.9 Pages: 1229-1236

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] AN INFINITE FAMILY OF CASSON HANDLES AND THE RASMUSSEN INVARIANT OF A KNOT2011

    • Author(s)
      田中 利史
    • Journal Title

      Journal of Knot Theory and its Ramifications

      Volume: 20 Pages: 1229-1236

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] An infinite family of prime satellite knots with the same Alexander polynomial2011

    • Author(s)
      田中 利史
    • Journal Title

      岐阜大学教育学部研究報告(自然科学)

      Volume: 36 Pages: 1-4

    • NAID

      110009422749

    • Related Report
      2011 Research-status Report
  • [Presentation] On slice knots and smooth 4-manifolds2013

    • Author(s)
      田中利史
    • Organizer
      第6回日本―メキシコ位相数学合同シンポジウム(同時開催)
    • Place of Presentation
      島根大学
    • Related Report
      2013 Final Research Report
  • [Presentation] On the maximal Thurston-Bennequin number for knots in a spatial graph2013

    • Author(s)
      田中利史
    • Organizer
      日本数学会トポロジー分科会
    • Place of Presentation
      京都大学
    • Related Report
      2013 Final Research Report
  • [Presentation] On the maximal Thurston-Bennequin number for knots in a Legendrian graph2013

    • Author(s)
      田中利史
    • Organizer
      研究集会「E-KOOKセミナー」
    • Place of Presentation
      大阪市立大学学術情報センター
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Jones polynomial of knots with symmetric union presentations2013

    • Author(s)
      田中利史
    • Organizer
      研究集会「The 9th East Asian School of Knots and Related Topics」
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2013 Final Research Report
  • [Presentation] On slice knots and smooth 4-manifolds2013

    • Author(s)
      Tanaka, Toshifumi
    • Organizer
      第6回日本―メキシコ位相数学合同シンポジウム
    • Place of Presentation
      島根大学
    • Related Report
      2013 Annual Research Report
  • [Presentation] On the Jones polynomial of knots with symmetric union presentations2013

    • Author(s)
      田中利史
    • Organizer
      The 9th East Asian School of Knots and Related Topics
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2012 Research-status Report
  • [Presentation] On the maximal Thurston-Bennequin number for knots in a Legendrian graph2013

    • Author(s)
      田中利史
    • Organizer
      E-KOOKセミナー
    • Place of Presentation
      大阪市立大学学術情報センター
    • Related Report
      2012 Research-status Report
  • [Presentation] On the maximal Thurston-Bennequin number for knots in a spatial graph2013

    • Author(s)
      田中利史
    • Organizer
      日本数学会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] On the Thurston-Bennequin number of Legendrian graphs2012

    • Author(s)
      田中利史
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2013 Final Research Report
  • [Presentation] On the Thurston-Bennequin number of Legendrian graphs2012

    • Author(s)
      田中 利史
    • Organizer
      研究集会「接触構造・特異点・微分方程式およびその周辺」(招待講演)
    • Place of Presentation
      鹿児島大学理学部
    • Related Report
      2011 Research-status Report
  • [Presentation] On symmetry of the Jones polynomial of ribbon knots2011

    • Author(s)
      田中利史
    • Organizer
      The 3rd KOOK-TAPU Joint Seminar on Knot Theory and Related Topics
    • Place of Presentation
      大阪市立大学
    • Related Report
      2013 Final Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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