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Study on Milnor invariants via finite type invariants

Research Project

Project/Area Number 26400081
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionTsuda College (2016)
Tokyo Gakugei University (2014-2015)

Principal Investigator

YASUHARA AKIRA  津田塾大学, 学芸学部, 教授 (60256625)

Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsミルナー不変量 / 絡み目 / 有限型不変量 / ストリング絡み目 / クローバー絡み目 / 被覆絡み目 / HOMFLYPT多項式
Outline of Final Research Achievements

For an n-component link, the Milnor invariant is defined for any finite sequence of numbers in {1,2,...,n}. It is very important in Knot (Link) Theory to study relations between Milnor invariant and other invariants. In this research, we give relations between Milnor invariant and HOMFLYPT polynomial, and Milnor invarinats and Milnor invariants for covering link (covering Milnor invarinats).

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (8 results)

All 2017 2016 2015 Other

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

  • [Journal Article] Milnor invariants of covering links2017

    • Author(s)
      Natsuka Kobayashi, Kodai Wada and Akira Yasuhara
    • Journal Title

      Topology and its Applications

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Milnor invariants of clover links2016

    • Author(s)
      Kodai Wada and Akira Yasuhara
    • Journal Title

      International Journal of Mathematics

      Volume: 27 Issue: 13 Pages: 1650108-1650108

    • DOI

      10.1142/s0129167x16501081

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Milnor invariants of length 2k+2 for links with vanishing Milnor invariants of length≦k2015

    • Author(s)
      Yuka Kotorii and Akira Yasuhara
    • Journal Title

      Topology and its Applications

      Volume: 184 Pages: 87-100

    • DOI

      10.1016/j.topol.2015.01.003

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Milnor invariants of clover links2016

    • Author(s)
      Kodai Wada
    • Organizer
      International Work- shop on Spatial Graphs 2016
    • Place of Presentation
      早稲田大学
    • Year and Date
      2016-08-03
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Milnor invariants of covering links2016

    • Author(s)
      Kodai Wada
    • Organizer
      Knots in the Triangle
    • Place of Presentation
      ノースカロライナ州立大学
    • Year and Date
      2016-04-29
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] The Milnor invariants of clover links2015

    • Author(s)
      Kodai Wada
    • Organizer
      Knots in Washington XLI
    • Place of Presentation
      ジョージ・ワシントン大学,ワシントンDC(アメリカ)
    • Year and Date
      2015-12-04
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] クローバー絡み目のミルナー不変量2015

    • Author(s)
      和田 康載
    • Organizer
      東北結び目セミナー 2015
    • Place of Presentation
      山形市保健センター 視聴覚室
    • Year and Date
      2015-10-23
    • Related Report
      2015 Research-status Report
  • [Remarks]

    • URL

      http://www.u-gakugei.ac.jp/~yasuhara

    • Related Report
      2015 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2018-03-22  

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