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A study of asymptotic behavior of HOMFLY and Kauffman polynomial

Research Project

Project/Area Number 19540071
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionKanazawa University

Principal Investigator

KAWAGOE Kenichi  Kanazawa University, 数物科学系, 講師 (50293337)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsトポロジー / 結び目 / 量子不変量
Research Abstract

近年、量子不変量の漸近挙動の研究が活発に行われている。そこではJones多項式をはじめ量子群からくるような量子不変量が使われている。今回はJones多項式を拡張した2変数多項式HOMFLY多項式の漸近挙動に関する研究を行った。これまでの漸近挙動とは異なる現象、すなわち体積以外の値に収束する例を発見し、2変数特有の現象を探ることに成功した。

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (9 results)

All 2009 2008 2007

All Journal Article (4 results) (of which Peer Reviewed: 4 results) Presentation (5 results)

  • [Journal Article] q-Analogues of the Riemann zeta, the Dirichlet $L$-functions, and a crystal zeta function2008

    • Author(s)
      K. Kawagoe, M. Wakayama, Y. Yamasaki
    • Journal Title

      Forum Math. 20,no.1

      Pages: 1-26

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] q-Analogues of the Riemann zeta, the Dirichlet L-functions, and a crystal zeta function2008

    • Author(s)
      K. Kawagoe, M. Wakayama, Y. Yamasaki
    • Journal Title

      Forum mathematicum 20

      Pages: 1-26

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limits of the HOMFLY polynomials of the figure-eight knot2007

    • Author(s)
      K. Kawagoe
    • Journal Title

      Intelligence of low dimensional topology 2006

      Pages: 143-150

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limits of the HOMFLY polynomial of the figureeight knot2007

    • Author(s)
      Kenichi Kawagoe
    • Journal Title

      Intelligence of the low dimensional topology

      Pages: 143-150

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] A homological representation of Braid groups and the Alexander polynomial2009

    • Author(s)
      川越謙一
    • Organizer
      結び目の数学II
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2009-12-24
    • Related Report
      2009 Final Research Report
  • [Presentation] A homological representation of Braid groups and the Alexander polynomial2009

    • Author(s)
      川越謙一
    • Organizer
      結び目の数学II
    • Place of Presentation
      早稲田大学 (東京都)
    • Year and Date
      2009-12-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] On limits of HOMFLY polynomials of knots and links2009

    • Author(s)
      川越謙一
    • Organizer
      トポロジーとコンピュータ2009
    • Place of Presentation
      東工大(東京都)
    • Year and Date
      2009-08-21
    • Related Report
      2009 Final Research Report
  • [Presentation] Homological representation of the Hecke algebras and the Temperley-Lieb algebras2009

    • Author(s)
      川越謙一
    • Organizer
      Korea-Japan Workshop on Algebra and Combinatorics
    • Place of Presentation
      釜山大学(韓国)
    • Year and Date
      2009-02-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Homological representation of the Hecke algebras and the Temperley-Lieb algebras2008

    • Author(s)
      川越謙一
    • Organizer
      結び目の数学
    • Place of Presentation
      東京女子大学(東京都)
    • Year and Date
      2008-12-24
    • Related Report
      2009 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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