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polynomial invariants of knots and related theory

Research Project

Project/Area Number 19740035
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionOsaka City University (2008)
Kyoto University (2007)

Principal Investigator

STOIMENOW Alexander  Osaka City University (60444452)

Project Period (FY) 2007 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥1,510,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥600,000 (Direct Cost: ¥600,000)
Keywordsbraid group / archiral knot / Hecke algebra / link polynomial / 組紐群 / 表現 / Lie群 / 絡み目 / unitary / 稠密 / Vassiliev invariants / Mutants / hyperbolic volume / slice / Graph
Research Abstract

15以上の各奇数交点数でのachiralな結び目の構成を完成した.
「行列-不・量-対数は'曲体"で直'的に近'される」という予想を-\'きにδ証明した.BurauとLawrence-Krammer現の稠密性,非自明なJones
多項式の問題と幾何的な性質を持つ閉じた3次組み紐についても研究を行った.

Report

(3 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report

Research Products

(18 results)

All 2009 2008 2007 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (4 results) Remarks (3 results)

  • [Journal Article] Bennequin's inequality and the positivity of the signature2008

    • Author(s)
      Stoimenow A
    • Journal Title

      Trans. Amer. Math. Soc 360(10)

      Pages: 5173-5199

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tait's conjectures and odd crossing number amphicheiral knots2008

    • Author(s)
      Stoimenow A
    • Journal Title

      Bull. Amer. Math. Soc. (N.S.) 45(2)

      Pages: 285-291

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Bennequin's inequality and the positivity of the signature2008

    • Author(s)
      A. Stoimenow
    • Journal Title

      Trans. Amer. Math. Soc 360(10)

      Pages: 5173-5199

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tait's conjectures and odd crossing number amphicheiral knots2008

    • Author(s)
      A. Stoimenow
    • Journal Title

      Bull. Amer. Math. Soc 45(3)

      Pages: 285-291

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions, Fibonacci numbers and rational knots, J.2007

    • Author(s)
      Stoimenow A
    • Journal Title

      Algebra 310(2)

      Pages: 491-525

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Square numbers and polynomial invariants of archiral knots2007

    • Author(s)
      Stoimenow A,
    • Journal Title

      Math. Z. 255(4)

      Pages: 703-719

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On cabled knots and Vassiliev invariants (not) contained in knot polynomials2007

    • Author(s)
      Stoimenow A,
    • Journal Title

      Canad. J. Math., 59(2)

      Pages: 418-448

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Graphs, determinants of knots and hyperbolic volume2007

    • Author(s)
      Stoimenow A,
    • Journal Title

      Pacific J. Math 232(2)

      Pages: 423-451

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generating functions, Fibonacci numbers and rational knots2007

    • Author(s)
      A. Stoimenow
    • Journal Title

      J. Algebra 310(2)

      Pages: 491-525

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Square numbers and polynomial invariants of archiral knots2007

    • Author(s)
      A. Stoimenow
    • Journal Title

      Math. Z. 255(4)

      Pages: 703-719

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On cabled knots and Vassiliev invariants (not) contained in knot polynomials2007

    • Author(s)
      A. Stoimenow
    • Journal Title

      Canad. J. Math. 59(2)

      Pages: 418-448

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Lie groups Burau representation, and non-conjugate braids with the same closure link2009

    • Author(s)
      Stoimenow A
    • Organizer
      The Fifth East Asia School of Knots and Related Topics
    • Place of Presentation
      慶州,韓国
    • Related Report
      2008 Final Research Report
  • [Presentation] Lie groups, Burau representation, and non-conjueate braids with the same closure link2008

    • Author(s)
      A. Stoimenow
    • Organizer
      The First Topology Workshop KAIST
    • Place of Presentation
      KAIST, 大田, 韓国
    • Year and Date
      2008-08-13
    • Related Report
      2008 Annual Research Report
  • [Presentation] Lie groups, Burau representation, and non-conjugate braids with the same closure link2008

    • Author(s)
      Stoimenow A
    • Organizer
      The First Topology Workshop KAIST
    • Place of Presentation
      韓国
    • Related Report
      2008 Final Research Report
  • [Presentation] Hecke algebra representations of braid groups and a conjecture of Jones2007

    • Author(s)
      A. Stoimenow
    • Organizer
      研究集会「結び目のトポロジーX」
    • Place of Presentation
      東京女子大学
    • Year and Date
      2007-12-24
    • Related Report
      2007 Annual Research Report
  • [Remarks]

    • URL

      http://mathsci.kaist.ac.kr/~stoimeno/

    • Related Report
      2008 Final Research Report
  • [Remarks]

    • URL

      http://mathsci.kaist.ac.kr/~stoimeno/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://math01.sci.osaka-cu.ac.jp/~stoimenow/

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-03-31   Modified: 2016-04-21  

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