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OnMilnorinvariantsandclassificationoflinksunder freeselfCn-equivalence

Research Project

Project/Area Number 22540104
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionOsaka Institute of Technology

Principal Investigator

SHIBUYA Tetsuo  大阪工業大学, 工学部, 教授 (00162652)

Co-Investigator(Kenkyū-buntansha) TSUKAMOTO Tatsuya  大阪工業大学, 工学部, 准教授 (10350480)
Co-Investigator(Renkei-kenkyūsha) YASUHARA Akira  東京学芸大学, 教育学部, 教授 (60256625)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords位相幾何学 / 結び目理論 / 結び目 / 素性 / スクエア結び目 / 幾何学 / トポロジー
Research Abstract

We introduced simple ribbon moves, and as their extension, simpleribbon fusions toward a systematic construction of ribbon links inspired by Milnor links.Then we studied the effect if we apply them to links, especially on disconnectivity numbersof link introduced by Goldberg and v-th genus, which is a refinement of general genus. Infact, we showed that simple ribbon fusions (moves) never increase the disconnectivitynumbers of links, and never decrease the v-th genus of links.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (13 results)

All 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (8 results)

  • [Journal Article] On non-self local moves2012

    • Author(s)
      Y. Nakanishi, T. Shibuya, T. Tsukamoto, and A. Yasuhara
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 21-4 Issue: 04 Pages: 125005511-9

    • DOI

      10.1142/s0218216511010097

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Selfdelta-equivalenceofalgebraically splitlinks2011

    • Author(s)
      T.Shibuya,T.Tsukamoto
    • Journal Title

      Mem.OsakaInst.Tech,SerA

      Volume: 56 Pages: 25-31

    • URL

      http://www.oit.ac.jp/japanese/toshokan/tosho/kiyou/rikouhen/56-1/03r.pdf

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On attendant graph of simple ribbon moves for links2011

    • Author(s)
      渋谷哲夫, 塚本達也
    • Journal Title

      Mem.Osaka Inst.Tech.Ser.A

      Volume: 56 Pages: 19-23

    • NAID

      40019056206

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Δ-equivalenceand Concordance for knots in the complement of a triviallink2010

    • Author(s)
      T.Fleming,T.Shibuya,T.Tsukamoto,A.Yasuhara,Homotopy
    • Journal Title

      Topologyandits Applications

      Volume: 157 Pages: 1215-1227

    • URL

      http://www.sciencedirect.com/science/article/pii/S0166864110000611

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Homotopy : Δ-equivalence and concordance for knots in the complement of atrivial link2010

    • Author(s)
      渋谷哲夫、塚本達也、安原晃
    • Journal Title

      Topology and its Applications

      Volume: 157 Pages: 1215-1227

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Simple ribbon fusions and genera of links2012

    • Author(s)
      K.Kishimoto,T.Shibuya,T.Tsukamoto
    • Organizer
      Knotsin WashingtonXXXV
    • Place of Presentation
      the George Washington University(USA)
    • Year and Date
      2012-12-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Simple ribbon fusions for linksII2012

    • Author(s)
      岸本健吾,渋谷哲夫,塚本達也
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-20
    • Related Report
      2012 Final Research Report
  • [Presentation] On simple ribbon move sonlinks2010

    • Author(s)
      小林一章,渋谷哲夫,塚本達也
    • Organizer
      E-KOOKSeminar2010
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2010-08-27
    • Related Report
      2012 Final Research Report
  • [Presentation] On simple ribbon moves on links2010

    • Author(s)
      塚本達也
    • Organizer
      E-KOOK Seminar 2010
    • Place of Presentation
      大阪市立大学(大阪府)(招待講演)
    • Year and Date
      2010-08-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Simple ribbon move sonlinks2010

    • Author(s)
      K.Kobayashi,T.Shibuya,T.Tsukamoto
    • Organizer
      Knotsin Polan dIII
    • Place of Presentation
      Bedlewo(Poland)
    • Year and Date
      2010-08-03
    • Related Report
      2012 Final Research Report
  • [Presentation] On simple ribbon moves on links2010

    • Author(s)
      塚本達也
    • Organizer
      Knots in poland III
    • Place of Presentation
      Math Institute at Bedlewo, Poland
    • Year and Date
      2010-08-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Simple ribbon fusions and genera of links

    • Author(s)
      岸本健吾,渋谷哲夫,塚本達也
    • Organizer
      Knots in Washington XXXV
    • Place of Presentation
      ジョージ・ワシントン大学(アメリカ合衆国)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Simple ribbon fusions for links II

    • Author(s)
      岸本健吾,渋谷哲夫,塚本達也
    • Organizer
      日本数学会2012年度秋季総合分科会
    • Place of Presentation
      九州大学(福岡県)
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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