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Study on the negativities of knots via open book decompositions of 3-manifolds

Research Project

Project/Area Number 18K13416
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11020:Geometry-related
Research InstitutionHiroshima Shudo University (2022)
Fisheries Research and Education Agency (2019-2021)
Tokyo University of Science (2018)

Principal Investigator

Tagami Keiji  広島修道大学, 経済科学部, 准教授 (60778174)

Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2021: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords絡み目 / 接触幾何学 / フラットプラミングバスケット / 接触構造 / 結び目 / ホップ不変量 / ゼロトレース / 3次元多様体 / オープンブック分解 / 正結び目
Outline of Final Research Achievements

A link is an embedding of a disjoint union of circles into a 3-manifold. In the case the number of the circles is one, a link is called a knot. Any 3-manifold can be represented as a surface bundle over a circle after removing a link from the 3-manifold. In the surface bundle, we obtain a new surface from a fiber surface by adding some bands at the boundaries.
In this study, we focus on such surfaces and links appearing in their boundaries. In particular, we explain relations between such a surface and its boundary by utilizing an inequality.

Academic Significance and Societal Importance of the Research Achievements

本研究の学術的意義として、絡み目と三次元多様体の接触構造の関係の記述が挙げられる。
古くから、三次元多様体は結び目を用いて研究されており、その接触構造についても例外ではなかった。本研究ではその流れを汲み、フラットプラミングバスケットと呼ばれる、接触幾何学と相性の良い曲面に着目し、その境界に現れる絡み目の性質(特に負値性)とフラットプラミングバスケットのトポロジーを関連付けた。それは従来の研究にない新しい点であり、学術的意義の一つとして考えられる。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (10 results)

All 2022 2021 2020 2019 2018

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (5 results) (of which Invited: 1 results)

  • [Journal Article] Notes on constructions of knots with the same trace2022

    • Author(s)
      Tagami Keiji
    • Journal Title

      Hiroshima Mathematical Journal

      Volume: 52 Issue: 1 Pages: 1-15

    • DOI

      10.32917/h2021005

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Knots with infinitely many non-characterizing slopes2021

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

      Kodai Mathematical Journal

      Volume: 44 Issue: 3 Pages: 395-421

    • DOI

      10.2996/kmj/kmj44301

    • NAID

      130008114210

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on stabilization heights of fiber surfaces and the Hopf invariants2021

    • Author(s)
      Tagami Keiji
    • Journal Title

      Bulletin of the Korean Mathematical Society

      Volume: 58 Pages: 1097-1107

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Flat plumbing basket and contact structure2021

    • Author(s)
      Ito Tetsuya、Tagami Keiji
    • Journal Title

      Journal of Knot Theory and Its Ramifications

      Volume: 30 Issue: 02 Pages: 2150010-2150010

    • DOI

      10.1142/s0218216521500103

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the Lagrangian fillability of almost positive links2019

    • Author(s)
      Keiji Tagami
    • Journal Title

      Journal of Korean Mathematical Society

      Volume: 56 Pages: 789-804

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Presentation] Annulus presentation and dualizable pattern2021

    • Author(s)
      Tagami Keiji
    • Organizer
      Intelligence of Low-dimensional Topology
    • Related Report
      2021 Research-status Report
  • [Presentation] 結び目のアニュラス表示から得られる双対化可能パターンの自然性2021

    • Author(s)
      田神慶士
    • Organizer
      2021年度日本数学会 年会
    • Related Report
      2020 Research-status Report
  • [Presentation] 0-トレースが等しい結び目の組を構成する3 つの方法とその関係2020

    • Author(s)
      田神慶士
    • Organizer
      大阪大学トポロジーセミ ナー
    • Related Report
      2020 Research-status Report
  • [Presentation] アニュラス表示から構成されるdualizable パターン2020

    • Author(s)
      田神慶士
    • Organizer
      N-KOOK セミナー
    • Related Report
      2020 Research-status Report
  • [Presentation] 絡み目のフラットプラミングバスケット表示と接触構造2018

    • Author(s)
      田神慶士
    • Organizer
      微分トポロジー
    • Related Report
      2018 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2024-01-30  

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