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Study on on properties and an extension of series and functions obtained from the quantum invariant of rational homology 3-shperes

Research Project

Project/Area Number 25400094
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

TAKATA Toshie  九州大学, 数理学研究院, 准教授 (40253398)

Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords結び目・3次元多様体の量子不変量 / トポロジー / 量子不変量 / colored Jones polynomial / free energy / 量子摂動的不変量
Outline of Final Research Achievements

We obtained a result that the second coefficient is presented by a constant multiple of the square root of the twisted Reidemeister torsion as N goes to the infinity in the asymptotic expansion of N colored Jones polynomial of a 2-bridge knots and SU(2) invariant of some hyperbolic 3-manifolds obtained by surgery along the figure-eight knot, by joint works with T. Ohtsuki.
We verified the slope conjecture for graph knots, i.e. knots whose Gromov volume vanish, by a joint work with K. Motegi.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (13 results)

All 2017 2016 2015 2014 2013

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 1 results) Presentation (10 results) (of which Int'l Joint Research: 2 results,  Invited: 10 results) Funded Workshop (1 results)

  • [Journal Article] The slope conjecture for graph knots2017

    • Author(s)
      茂手木公彦、高田敏恵
    • Journal Title

      Math. Proc. Cambridge Philos. Soc.

      Volume: 162 Issue: 3 Pages: 383-392

    • DOI

      10.1017/s0305004116000566

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots2015

    • Author(s)
      大槻知忠, 高田敏恵
    • Journal Title

      Geometry and Topology

      Volume: 19 Issue: 2 Pages: 853-952

    • DOI

      10.2140/gt.2015.19.853

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] The slope conjecture and periodic construction2017

    • Author(s)
      高田敏恵
    • Organizer
      Low dimensional topology and number theory IX
    • Place of Presentation
      九州大学産学官連携イノベーションプラザ
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The slope conjecture for graph knots2016

    • Author(s)
      高田敏恵
    • Organizer
      拡大KOOKセミナー2016
    • Place of Presentation
      大阪電気通信大学
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] On the asymptotic expansions of the Kashaev invariant of some hyperbolic knots with 8 crossings2016

    • Author(s)
      高田敏恵
    • Organizer
      Workshop on Volume Conjecture and Quantum Topology
    • Place of Presentation
      早稲田大学
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The slope conjecture and periodic construction2016

    • Author(s)
      高田敏恵
    • Organizer
      東北結び目セミナー2016
    • Place of Presentation
      東北大学
    • Related Report
      2016 Annual Research Report
    • Invited
  • [Presentation] The slope conjecture for graph knots2015

    • Author(s)
      高田敏恵
    • Organizer
      拡大KOOKセミナー2015
    • Place of Presentation
      神戸大学
    • Year and Date
      2015-08-19
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots2015

    • Author(s)
      高田敏恵
    • Organizer
      Intelligence of Low-dimensional Topology
    • Place of Presentation
      京都大学 数理解析研究所
    • Year and Date
      2015-05-22
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] On the slope conjecture for cables of knots2014

    • Author(s)
      高田敏恵
    • Organizer
      2014年度東北結び目セミナー
    • Place of Presentation
      秋田市カレッジプラザ
    • Year and Date
      2014-10-19
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots2014

    • Author(s)
      高田敏恵
    • Organizer
      Quantum Topology and Physics 2014 Fukuoka
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2014-09-18
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 結び目群の表現とcolored Jones polynomial2013

    • Author(s)
      高田 敏恵
    • Organizer
      群と幾何学の展望
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] On the Kashaev invariant and the twisted Reidemeister torsion of two-bridge knots2013

    • Author(s)
      高田 敏恵
    • Organizer
      曲面の写像類群に関する幾何と代数
    • Place of Presentation
      文部科学省共済組合箱根宿泊所四季の湯強羅星雲荘
    • Related Report
      2013 Research-status Report
    • Invited
  • [Funded Workshop] Braids, Configuration Spaces, and Quantum Topology2015

    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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