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Orientations and invariants of handlebody-knots

Research Project

Project/Area Number 15K04866
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
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) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords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 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: We defined a multiple conjugation biquandle, which is a biquandle with partial group operations. We introduced the (co)homology theory for a multiple conjugation biquandle.

Report

(4 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (7 results)

All 2018 2017 2016 2015

All Journal Article (4 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 4 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (3 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results)

  • [Journal Article] A multiple conjugation biquandle and handlebody-links2018

    • Author(s)
      Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro
    • Journal Title

      Hiroshima Math. J.

      Volume: 48 Pages: 89-117

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Homology for quandles with partial group operations2017

    • Author(s)
      Scott Carter, Atsushi Ishii, Masahico Saito, Kokoro Tanaka
    • Journal Title

      Pacific J. Math.

      Volume: 287-1 Issue: 1 Pages: 19-48

    • DOI

      10.2140/pjm.2017.287.19

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The Markov theorems for spatial graphs and handlebody-knots with Y-orientations2015

    • Author(s)
      Atsushi Ishii
    • Journal Title

      Internat. J. Math.

      Volume: 26 Issue: 14 Pages: 1550116-1550116

    • DOI

      10.1142/s0129167x15501165

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] A multiple conjugation quandle and handlebody-knots2015

    • Author(s)
      Atsushi Ishii
    • Journal Title

      Topology Appl.

      Volume: 196 Pages: 492-500

    • DOI

      10.1016/j.topol.2015.05.029

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] An augmented Alexander matrix and an affine extension of a quandle2018

    • Author(s)
      Atsushi Ishii
    • Organizer
      Branched Coverings, Degenerations, and Related Topics 2018
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Parallel biquandle colorings for handlebody-knots and spatial graphs2016

    • Author(s)
      Atsushi Ishii
    • Organizer
      International Workshop on Spatial Graphs 2016
    • Place of Presentation
      早稲田大学(東京都新宿区)
    • Year and Date
      2016-08-03
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The Markov theorem for spatial graphs and handlebody-knots2015

    • Author(s)
      Atsushi Ishii
    • Organizer
      AMS Sectional Meeting
    • Place of Presentation
      California State University (U.S.A)
    • Year and Date
      2015-10-24
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited

URL: 

Published: 2015-04-16   Modified: 2019-03-29  

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