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Handlebody-knots and invariants

Research Project

Project/Area Number 24740037
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionUniversity of Tsukuba

Principal Investigator

ISHII Atsushi  筑波大学, 数理物質系, 講師 (00531451)

Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords位相幾何学 / 結び目理論
Outline of Final Research Achievements

A handlebody-link is a disjoint union of handlebodies embedded in the 3-sphere. A handlebody-knot is a one component handlebody-link. A genus one handlebody-knot corresponds to a usual knot. That is, a handlebody-knot is a natural generalization of a knot. The results of this study are as follows: The (co)homology theory for multiple conjugation quandles, which is a quandle with partial group operations, was introduced.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (7 results)

All 2015 2014 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 1 results) Presentation (2 results) (of which Invited: 2 results)

  • [Journal Article] Handlebody-knot invariants derived from unimodular Hopf algebras2014

    • Author(s)
      Atsushi Ishii, Akira Masuoka
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 23 Issue: 07 Pages: 1460001-1460024

    • DOI

      10.1142/s0218216514600013

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] An operator invariant for handlebody-knots2012

    • Author(s)
      Kai Ishihara, Atsushi Ishii
    • Journal Title

      Fund. Math.

      Volume: 217 Issue: 3 Pages: 233-247

    • DOI

      10.4064/fm217-3-3

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Quandle cocycle invariants for spatial graphs and knotted handlebodies2012

    • Author(s)
      Atsushi Ishii, Masahide Iwakiri
    • Journal Title

      Canad. J. Math.

      Volume: 64 Pages: 102-122

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A table of genus two handlebody-knots up to six crossings2012

    • Author(s)
      Atsushi Ishii, Kengo Kishimoto, Hiromasa Moriuchi, Masaaki Suzuki
    • Journal Title

      J. Knot Theory Ramifications

      Volume: 21 Issue: 04 Pages: 1250035-1250035

    • DOI

      10.1142/s0218216511009893

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map2012

    • Author(s)
      Atsushi Ishii, Kengo Kishimoto
    • Journal Title

      Topology Appl.

      Volume: 159 Issue: 4 Pages: 1115-1121

    • DOI

      10.1016/j.topol.2011.11.018

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] The skein index and Fox p-colorings2015

    • Author(s)
      Atsushi Ishii
    • Organizer
      Knots and Manifolds
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2015-02-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Multiple conjugation quandles and handlebody-knots

    • Author(s)
      Atsushi Ishii
    • Organizer
      2013 TAPU Workshop on Knot Theory and Related Topics, National Institute for Mathematical Sciences
    • Place of Presentation
      Daejeon, Korea
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2013-05-31   Modified: 2019-07-29  

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