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2012 Fiscal Year Final Research Report

Research on representation theoretic structures of unknot detectors

Research Project

  • PDF
Project/Area Number 22740048
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionMeijo University

Principal Investigator

NAGASATO Fumikazu  名城大学, 理工学部, 准教授 (30513634)

Project Period (FY) 2010 – 2012
Keywords結び目 / 結び目群 / character variety / Chebyshev 多項式 / trace-free 表現
Research Abstract

This study is concerned with researches on representation theoretic structures of unknot detectors. In particular, we focus on the geometric structures on the algebraic subset S0(K) of the character variety X(K) defined by trace-free condition. In the researches, we found a family of polynomials whose zero-locus gives the set S0(K). Applying the polynomials, we found a filtration of S0(K) each of whose filters gives a knot invariant. This fact reveals a relationship between S0(K) and the abelian knot contact homology. The methods used in these researches can be also applied to determine some minimal elements for a partial ordering of prime knots.

  • Research Products

    (11 results)

All 2012 2011 2010 Other

All Journal Article (4 results) (of which Peer Reviewed: 3 results) Presentation (6 results) Remarks (1 results)

  • [Journal Article] On minimal elements for a partial order of prime knots2012

    • Author(s)
      Fumikazu Nagasato
    • Journal Title

      Topology and its Applications

      Volume: Vol.159 Pages: 1059-1063

    • Peer Reviewed
  • [Journal Article] YoshikazuYamaguchi,On the geometry of the slice of trace-free SL(2,C)-characters of a knot group2012

    • Author(s)
      Fumikazu Nagasato
    • Journal Title

      Mathematische Annalen

      Volume: Vol.354 Pages: 967-1002

    • Peer Reviewed
  • [Journal Article] On the character rings of twist knots2011

    • Author(s)
      Fumikazu Nagasato
    • Journal Title

      Bulletin of the Korean Mathematical Society

      Volume: Vol.48 No.3 Pages: 469-474

    • Peer Reviewed
  • [Journal Article] On the trace-free characters

    • Author(s)
      Fumikazu Nagasato
    • Journal Title

      RIMS Kokyuroku

  • [Presentation] On trace-free characters and abelian knot contact homolog2012

    • Author(s)
      Fumikazu Nagasato
    • Organizer
      RIMS Seminar『Representation spaces, twisted topological invariants andgeometric structures of 3-manifolds』
    • Place of Presentation
      GoraSeiunso
    • Year and Date
      20120528-0601
  • [Presentation] On the trace-free characters of knot groups2012

    • Author(s)
      Fumikazu Nagasato
    • Organizer
      UCSB Topology Seminar, University ofCalifornia
    • Place of Presentation
      Santa Barbara
    • Year and Date
      2012-10-31
  • [Presentation] On the space of colorings of a knot2012

    • Author(s)
      長郷文和
    • Organizer
      研究会「2012 琉球結び目セミナー」
    • Place of Presentation
      那覇市伝統工芸館
    • Year and Date
      2012-09-03
  • [Presentation] On minimal elements for a partial order of prime knots2012

    • Author(s)
      長郷文和
    • Organizer
      九州大学トポロジーセミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2012-02-23
  • [Presentation] On metabelian representations and their applications2011

    • Author(s)
      長郷文和
    • Organizer
      研究会「2011 琉球結び目セミナー」
    • Place of Presentation
      那覇市伝統工芸館
    • Year and Date
      2011-09-07
  • [Presentation] On minimal elements for a partial order of prime knots2010

    • Author(s)
      Fumikazu Nagasato
    • Organizer
      International Conference Japan-Mexico on Topology and its Applications
    • Place of Presentation
      Universidad de Colima, Mexico
    • Year and Date
      2010-09-28
  • [Remarks]

    • URL

      http://ccmath.meijo-u.ac.jp/~fukky/

URL: 

Published: 2014-08-29  

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