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Study of positive knots via contact structures

Research Project

Project/Area Number 16H07230
Research Category

Grant-in-Aid for Research Activity Start-up

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo University of Science

Principal Investigator

Tagami Keiji  東京理科大学, 理工学部数学科, 助教 (60778174)

Project Period (FY) 2016-08-26 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords結び目 / 正結び目 / 接触構造 / ラグランジアン充填 / 正絡み目 / サーストン・ベネカン数
Outline of Final Research Achievements

A knot is a smooth embedding of a circle into the 3-dimensional Euclidean space. A knot is Lagrangian fillable if it bounds an oriented Lagrangian surface from below in the symplectisation of the standard contact structure of the 3-dimensional Euclidean space.
Hayden and Sabloff proved that any positive knot is Lagrangian fillable. Inspired by their work, in this study, I investigated relations between the Lagrangian fillability and the positivity of knots. As a result, I proved that (1) any almost positive knot with a certain condition on its Seifert graph is Lagrangian fillable, (2) any alternating and Lagrangian fillable knot is positive.

Report

(3 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Annual Research Report
  • Research Products

    (2 results)

All 2017

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (1 results)

  • [Journal Article] Characterization of Positive Links and the s-invariant for Links2017

    • Author(s)
      Tetsuya Abe and Keiji Tagami
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 69 Issue: 6 Pages: 1201-1218

    • DOI

      10.4153/cjm-2016-030-7

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Presentation] 結び目とラグランジアン充填2017

    • Author(s)
      田神慶士
    • Organizer
      関東若手幾何セミナー
    • Related Report
      2017 Annual Research Report

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Published: 2016-09-02   Modified: 2019-03-29  

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