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Quandle theory and surface-link invariants

Research Project

Project/Area Number 23840040
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionJapan Women's University

Principal Investigator

OSHIRO Kanako  日本女子大学, 理学部, 助教 (90609091)

Project Period (FY) 2011 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords結び目 / 曲面結び目 / カンドル / G-family of quandles / 曲面絡み目 / ラック / Roseman 変形 / 三重点 / handlebody-knot / Linear Alexander quandle / Minimal number of colors
Research Abstract

In this research, we gave the following results: (1) We gave an evaluation for the minimum number of colors for surface-knots. (2) We defined a G-family of quandles, and constructed an invariant for handlebody-knots. (3) We researched about the colorability with linear Alexander quandles. (4) We showed that rack colorings are invariant for 2-knots.

Report

(3 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • Research Products

    (32 results)

All 2013 2012 2011 Other

All Journal Article (7 results) (of which Peer Reviewed: 6 results) Presentation (24 results) (of which Invited: 2 results) Remarks (1 results)

  • [Journal Article] On linear n-colorings for knots2012

    • Author(s)
      Chuichiro Hayashi, Miwa Hayashi, Kanako Oshiro
    • Journal Title

      Journal of Knot Theory and its Ramifications 21

      Volume: 1250123 Pages: 13-13

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric quandle colorings for spatial graphs and handlebody-links2012

    • Author(s)
      Yeonhee Jang and Kanako Oshiro
    • Journal Title

      Journal of Knot Theory and its Ramifications 21

      Volume: 1250050 Pages: 16-16

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On pallets for Fox-colorings of spatial graphs2012

    • Author(s)
      Kanako Oshiro
    • Journal Title

      Topology and its Applications

      Volume: 159 Pages: 1092-1105

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On linear n-colorings for knots2012

    • Author(s)
      Chuichiro Hayashi, Miwa Hayashi and Kanako Oshiro
    • Journal Title

      Journal of Knot Theory and its Ramifications

      Volume: Vol.21, No.14 Issue: 14 Pages: 13-13

    • DOI

      10.1142/s0218216512501234

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On pallets for Fox colorings of spatial graphs2012

    • Author(s)
      Kanako Oshiro
    • Journal Title

      Topology and its Applications

      Volume: 159 Issue: 4 Pages: 1092-1105

    • DOI

      10.1016/j.topol.2011.11.025

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symmetric quandle colorings for spatial graphs and handlebody-links2012

    • Author(s)
      Yeonhee Jang, Kanako Oshiro
    • Journal Title

      Journal of Knot Theory and its Ramifications

      Volume: (in press) Issue: 04 Pages: 595-608

    • DOI

      10.1142/s0218216511010024

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pallets and coloring invariants for spatial graphs2011

    • Author(s)
      Kanako Oshiro
    • Journal Title

      数理解析研究所講究録

      Volume: 1766 Pages: 72-80

    • Related Report
      2011 Annual Research Report
  • [Presentation] On rack colorings for surface-knot diagrams without branch points2013

    • Author(s)
      Kanako Oshiro
    • Organizer
      The 9th East Asian School of Knots and Related Topics
    • Place of Presentation
      東京大学
    • Related Report
      2012 Annual Research Report 2012 Final Research Report
  • [Presentation] パレットを使った空間グラフ不変量について2012

    • Author(s)
      大城佳奈子
    • Organizer
      研究集会「Hurwitz action」
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2012-01-29
    • Related Report
      2011 Annual Research Report
  • [Presentation] Minimal numbers of colors for surface-knots and quandle cocycle invariants2012

    • Author(s)
      大城佳奈子
    • Organizer
      Friday seminar on Knot Theory
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2012-01-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] パレットを使った空 間グラフ不変量と Hurwitz action について2012

    • Author(s)
      Kanako Oshiro
    • Organizer
      研究集会「Hurwitz action」
    • Related Report
      2012 Final Research Report
  • [Presentation] On linear colorings for knots2012

    • Author(s)
      Kanako Oshiro
    • Organizer
      広島大学トポロジー・幾何セ ミナー
    • Place of Presentation
      広島大学
    • Related Report
      2012 Final Research Report
  • [Presentation] A G-family of quandles and handlebody-link invariants2012

    • Author(s)
      Kanako Oshiro
    • Organizer
      6th European Congress of Mathematics
    • Place of Presentation
      Krakow (Poland)
    • Related Report
      2012 Final Research Report
  • [Presentation] n-twist-spun trefoil のカンドル彩色について2012

    • Author(s)
      Kanako Oshiro
    • Organizer
      2012琉球結び目セミナー
    • Place of Presentation
      那覇市伝統工芸会議場
    • Related Report
      2012 Final Research Report
  • [Presentation] 2次元結び目のラック 彩色数について2012

    • Author(s)
      Kanako Oshiro
    • Organizer
      トポロジーセミナー
    • Place of Presentation
      東京女子大学
    • Related Report
      2012 Final Research Report
  • [Presentation] On linear colorings for knots2012

    • Author(s)
      大城佳奈子
    • Organizer
      広島大学トポロジー・幾何セミナー
    • Place of Presentation
      広島大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] A G-family of quandles and handlebody-link invariants2012

    • Author(s)
      大城佳奈子
    • Organizer
      6th European Congress of Mathematics
    • Place of Presentation
      Cracow, Poland
    • Related Report
      2012 Annual Research Report
  • [Presentation] n-twist-spun trefoil のカンドル彩色について2012

    • Author(s)
      大城佳奈子
    • Organizer
      2012 琉球結び目セミナー
    • Place of Presentation
      那覇市伝統工芸会議場
    • Related Report
      2012 Annual Research Report
  • [Presentation] 2次元結び目のラック彩色数について2012

    • Author(s)
      大城佳奈子
    • Organizer
      東京女子大学トポロジーセミナー
    • Place of Presentation
      東京女子大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Minimal numbers of colors and quandle cocycle invariants for surface-knots2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      Claremont Topology Seminar
    • Place of Presentation
      Pomona College (USA)
    • Year and Date
      2011-12-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] Minimal numbers of colors for surface-knots and quandle cocycle invariants2011

    • Author(s)
      大城佳奈子
    • Organizer
      研究集会「4次元トポロジー」
    • Place of Presentation
      広島大学
    • Year and Date
      2011-11-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] カントルと結び目不変量2011

    • Author(s)
      大城佳奈子
    • Organizer
      理学セミナー
    • Place of Presentation
      日本女子大学
    • Year and Date
      2011-10-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Minimal numbers of colors for surface-knots and quandle cocycle invariants2011

    • Author(s)
      大城佳奈子
    • Organizer
      琉球結び目セミナー
    • Place of Presentation
      那覇市伝統工芸館会議場
    • Year and Date
      2011-09-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] Pallets and coloring invariants for spatial graphs2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      Intelligence of Low-dimensional Topology
    • Place of Presentation
      京都大学
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Pallets of quandles2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      トポロジーセミナー
    • Place of Presentation
      東京工業大学
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Minimal number of colors and quandle cocycle invariants of surface-knots2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      トポロジーセミナー
    • Place of Presentation
      東京女子大学
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Pallets of quandles and coloring invariants of spatial graphs2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      第58回トポロジーシンポジウム
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Minimal number of colors for surface-knots and quandle cocycle invariants2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      琉球結び目セミナー
    • Place of Presentation
      那覇市伝統工芸会議場
    • Related Report
      2012 Final Research Report
  • [Presentation] カンドルと結び目不 変量2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      理学セミナー
    • Place of Presentation
      日本女子大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Minimal numbers of colors for surface-knots and quandle cocycle invariants2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      研究集会「4 次元のトポロジー」
    • Place of Presentation
      広島大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Minimal numbers of colors and quandle cocycle invariants for surface-knots2011

    • Author(s)
      Kanako Oshiro
    • Organizer
      Claremont Topology Semina
    • Place of Presentation
      Pomona College
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://pweb.sophia.ac.jp/oshirok/

    • Related Report
      2012 Final Research Report

URL: 

Published: 2011-09-05   Modified: 2019-07-29  

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