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Studies on band surgery and Dehn surgery on links

Research Project

Project/Area Number 19K03483
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11020:Geometry-related
Research InstitutionKindai University

Principal Investigator

Jong In Dae  近畿大学, 理工学部, 准教授 (30587788)

Project Period (FY) 2019-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2021: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2020: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Keywordsデーン手術 / 矯飾的デーン手術 / 例外的デーン手術 / 結び目 / 絡み目 / 局所変形操作 / モンテシノス結び目 / 交代結び目 / 2橋結び目 / 2橋絡み目 / バンド変形 / 低次元トポロジー
Outline of Research at the Start

絡み目のバンド変形は3次元球面の2重分岐被覆空間のデーン手術に対応します.特に,鏡像を生むバンド変形や結び目の型を変えないバンド変形は,これまであまり成されていない両手型3次元多様体の研究や,低次元トポロジー分野の重要な未解決予想であるコスメティック手術予想に直結します.本研究では上述の事実に基づき,結び目のバンド変形とデーン手術を通して低次元トポロジー・結び目理論の研究を行います.

Outline of Final Research Achievements

1) We prove that any non-trivial two-bridge knot admit no purely cosmetic surgery pairs. The paper containing the result had published in a refereed journal as a collaboration paper with Kazuhiro Ichihara, Toshio Saito, and Thomas Mattman. 2) We calculate several invariants to show alternating knots and Montesinos knots admit no purely cosmetic surgeries. We obtain a partial result for this study. 3) We give a complete list of hyperbolic two-bridge links which can admit complete exceptional surgeries. The paper containing the result had submitted to a refereed journal as a collaboration paper with Kazuhiro Ichihara and Hidetoshi Masai.

Academic Significance and Societal Importance of the Research Achievements

本研究で得られた成果のうち,学術雑誌に掲載された論文「Two-bridge knots admit no purely cosmetic surgeries」は,今後のデーン手術研究,特に矯飾的デーン手術研究における重要なマイルストーンとなります.さまざまな不変量の計算を駆使して全ての2橋結び目に対して未解決問題が解決できたことは,結果自体が重要であることに加え,研究手法として1つの道筋を構成したことに意義があります.

Report

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

    (10 results)

All 2021 2020 2019 Other

All Journal Article (2 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 2 results) Presentation (6 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results) Remarks (2 results)

  • [Journal Article] Two-bridge knots admit no purely cosmetic surgeries2021

    • Author(s)
      Ichihara Kazuhiro、Jong In Dae、Mattman Thomas W、Saito Toshio
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 21 Issue: 5 Pages: 2411-2424

    • DOI

      10.2140/agt.2021.21.2411

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Two-bridge knots admit no purely cosmetic surgeries2021

    • Author(s)
      Kazuhiro Ichihara, In Dae Jong, Thomas Mattman, Toshio Saito
    • Journal Title

      Algebraic & Geometric Topology

      Volume: 掲載決定

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Alternating Montesinos knots admit no purely cosmetic surgeries2021

    • Author(s)
      鄭仁大
    • Organizer
      研究集会「拡大KOOKセミナー2021」
    • Related Report
      2021 Research-status Report
  • [Presentation] Alternating Montesinos knots admit no purely cosmetic surgeries2021

    • Author(s)
      鄭仁大
    • Organizer
      東京女子大学トポロジーセミナー
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] Complete exceptional surgeries on two-bridge links2021

    • Author(s)
      In Dae Jong and Hidetoshi Masai
    • Organizer
      The 16th East Asian Conference on Geometric Topology
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On purely cosmetic surgeries and Montesinos knots2020

    • Author(s)
      鄭仁大
    • Organizer
      東北結び目セミナー2020
    • Related Report
      2020 Research-status Report
  • [Presentation] Two-bridge knots admit no purely cosmetic surgeries2020

    • Author(s)
      市原一裕,斎藤敏夫,鄭仁大,T. W. Mattman
    • Organizer
      日本数学会2020年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] Complete exceptional surgeries on two-bridge links2019

    • Author(s)
      鄭 仁大
    • Organizer
      Friday Seminar on Knot Theory
    • Related Report
      2019 Research-status Report
    • Invited
  • [Remarks] プレプリントサーバarXiv

    • URL

      https://arxiv.org/abs/1909.02340

    • Related Report
      2019 Research-status Report
  • [Remarks] プレプリントサーバarXiv

    • URL

      https://arxiv.org/abs/1909.11319

    • Related Report
      2019 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2024-01-30  

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