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On the Rasmussen (Beliakova-Wehrli) invariant for links

Research Project

Project/Area Number 23840021
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

ABE Tetsuya  京都大学, 数理解析研究所, 研究員(GCOE) (00614009)

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 / 絡み目 / ラスムッセン不変量 / Beliakova-Wehrli 不変量 / コバノフホモロジー / リーホモロジー / コンコーダンス群 / スライス結び目 / リボン結び目 / スライス・リボン予想 / ハンドル図式(カービー図式) / 4次元多様体 / カービー計算 / 低次元トポロジー / バンド手術
Research Abstract

We studied the Beliakova-Wehrli invariant for a link which is a generalization of the Rasmussen invariant for a knot. We also studied a slice knot which is closely related to the Rasmussen invariant.

Report

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

    (15 results)

All 2013 2012 2011 Other

All Journal Article (9 results) (of which Peer Reviewed: 7 results) Presentation (5 results) Remarks (1 results)

  • [Journal Article] Unoriented band-surgery on knots and links2013

    • Author(s)
      T.Abe, T. Kanenobu
    • Journal Title

      to appear in Kobe Journal of Mathematics

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Annulus twist and diffeomorphic 4-manifolds2013

    • Author(s)
      T.Abe, I. Jong, Y. Omae and M. Takeuchi
    • Journal Title

      Math. Proc. Cambridge Philos. Soc

      Pages: 1-17

    • URL

      http://arxiv.org/pdf/1209.0361v2.pdf

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Omae's knot and 12a990 are ribbon2012

    • Author(s)
      T.Abe and M. Tange
    • Journal Title

      RIMS Kokyuroku

      Volume: 1812 Pages: 34-42

    • URL

      http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/pdf/1812-04.pdf

    • Related Report
      2012 Final Research Report
  • [Journal Article] The unknotting number and band-unknotting number of a knot2012

    • Author(s)
      T.Abe, R. Hanaki and R. Higa
    • Journal Title

      Osaka J. Math

      Volume: 49 Pages: 523-550

    • NAID

      120005986505

    • URL

      http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.ojm/1340197938

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] State cycles which represent the canonical class of Lee's homology of a knot2012

    • Author(s)
      T.Abe
    • Journal Title

      Topology and its Applications

      Volume: Volume 159 Issue: 4 Pages: 1146-1158

    • DOI

      10.1016/j.topol.2011.11.042

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Omae's knot and 12a990 are ribbon2012

    • Author(s)
      T. Abe and M. Tange
    • Journal Title

      RIMS Kokyuroku

      Volume: 1812

    • Related Report
      2012 Annual Research Report
  • [Journal Article] The unknotting number and band-unknotting number of a knot2012

    • Author(s)
      Tetsuya Abe, Ryo Hanaki, Ryuji Higa
    • Journal Title

      Osaka J.Math.

      Volume: (印刷中)

    • NAID

      120005986505

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Rasmussen invariant of a homogeneous knot2011

    • Author(s)
      T.Abe
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: 139 Pages: 2647-2656

    • URL

      http://arxiv.org/pdf/1003.5392v1.pdf

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Rasmussen invariant of a homogeneous knot2011

    • Author(s)
      Tetsuya Abe
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 139 Pages: 2647-2656

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] Omae's knot and 12a990 are ribbon2012

    • Author(s)
      安部哲哉
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Annulus twists and diffeomorphic 4-manifolds2012

    • Author(s)
      Tetsuya Abe
    • Organizer
      The 6th European Congress of Mathematics, Jagellionian University
    • Place of Presentation
      Poland
    • Year and Date
      2012-07-05
    • Related Report
      2012 Final Research Report
  • [Presentation] Unoriented band surgery on knots and link2012

    • Author(s)
      安部哲哉
    • Organizer
      日本数学会春季総合分科会
    • Place of Presentation
      東京理科大学
    • Year and Date
      2012-03-26
    • Related Report
      2012 Final Research Report
  • [Presentation] Unoriented band surgery on knots and links2012

    • Author(s)
      Tetsuya Abe
    • Organizer
      日本数学会
    • Place of Presentation
      Tokyo(日本)
    • Year and Date
      2012-03-26
    • Related Report
      2011 Annual Research Report
  • [Presentation] Omae's knot and 12_a990 are ribbon2012

    • Author(s)
      安部哲哉
    • Organizer
      日本数学会 秋季総合分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://yumemusou.web.fc2.com

    • Related Report
      2011 Annual Research Report

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

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