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Surgery on 4-manifolds by exceptional Dehn surgery on 3-manifold

Research Project

Project/Area Number 16K05143
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionThe University of Electro-Communications

Principal Investigator

YAMADA Yuichi  電気通信大学, 大学院情報理工学研究科, 教授 (30303019)

Co-Investigator(Kenkyū-buntansha) 山口 耕平  電気通信大学, 大学院情報理工学研究科, 名誉教授 (00175655)
丹下 基生  筑波大学, 数理物質系, 准教授 (70452422)
Project Period (FY) 2016-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords3次元多様体 / 4次元多様体 / デーン手術 / 枠付き絡み目 / Kirby計算 / divide knot / レンズ空間 / 特異点論 / 幾何学 / トポロジー / ディバイド表示 / Kirby 計算
Outline of Final Research Achievements

Phenomenon that a Dehn surgery along a hyperbolic knot in the 3-shpere yields a non-hyperbolic manifold is called "exceptional surgery" and is a subject in the topology of low-dimensional manifolds. We are interested in construction and surgery on 4-manifolds related to exceptional Dehn surgeries. Results : Distributions of integral coefficient exceptional surgeries along Akbulut-Yasui link, including the Mazur link, are decided. Divide presentation of knots in the minor subfamily is considered, and is published in a paper. As research action, I attended almost all workshops "Differential topology” and "handle seminor".

Academic Significance and Societal Importance of the Research Achievements

低次元多様体のトポロジー分野において、3次元多様体論と4次元多様体論では様相が大きく異なる。筆者の研究の独創的な点として、その両方に興味を持って研究を進めてきた点が挙げられる。ただし最近の研究動向として両者の関連は急激に強くなっており、2000年代(~2010) に登場し急発展したヒーガード・フレアー理論はその典型的な事例といえる。例外的デーン手術から生じる4次元多様体には意外な具体例が多い。本研究の後半では、4次元多様体論の側で対合を持つ4次元コボルディズムへの興味が特に高まっていた。今後も地道な貢献を続けたい。

Report

(7 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (29 results)

All 2022 2021 2020 2019 2018 2017 2016 Other

All Journal Article (8 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 7 results,  Open Access: 2 results) Presentation (14 results) (of which Int'l Joint Research: 2 results,  Invited: 2 results) Remarks (5 results) Funded Workshop (2 results)

  • [Journal Article] The third term in lens surgery polynomials2021

    • Author(s)
      Motoo Tange
    • Journal Title

      Hiroshima Math. J.

      Volume: 51(1) Issue: 1 Pages: 101-109

    • DOI

      10.32917/h2020050

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Notes on Gompf's infinite order corks2021

    • Author(s)
      Motoo Tange
    • Journal Title

      Michigan Math. J.

      Volume: 70 Issue: 1 Pages: 3-21

    • DOI

      10.1307/mmj/1586419413

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Divide knot presentation of sporadic knots of Berge's lens space surgery2020

    • Author(s)
      Yuichi Yamada
    • Journal Title

      Kyungpook Math. J.

      Volume: 60(2)

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] The topology of the space of rational curves on a topic variety and related problems2019

    • Author(s)
      Kohhei Yamaguchi
    • Journal Title

      数理解析研究所講究録

      Volume: 2135 Pages: 63-69

    • Related Report
      2019 Research-status Report
  • [Journal Article] Exceptional Dehn surgeries along the Mazur link2018

    • Author(s)
      Yuichi YAMADA
    • Journal Title

      J. Gokova Geom. Topol. GGT

      Volume: 12

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The homotopy type of spaces of rational curves on a toric variety2018

    • Author(s)
      Kozlowski A.、Yamaguchi K.
    • Journal Title

      Topology and its Applications

      Volume: 249 Pages: 19-42

    • DOI

      10.1016/j.topol.2018.06.006

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Four-dimensional manifolds constructed by lens space surgeries of distinct types2017

    • Author(s)
      Motoo Tange and Yuichi Yamada
    • Journal Title

      J. of Knot Theory and its Ramifications

      Volume: 26 No.11 Issue: 11 Pages: 1750069-1750069

    • DOI

      10.1142/s0218216517500699

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The homotopy type of spaces of resultants of bounded multiplicity2017

    • Author(s)
      A. Kozlowski and K. Yamaguchi
    • Journal Title

      Topology and its Appl.

      Volume: 232 Pages: 112-139

    • DOI

      10.1016/j.topol.2017.10.002

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Divide knot presentation of Type 8 knots in Berge's lens space surgery2022

    • Author(s)
      Yamada Yuichi
    • Organizer
      The 17th East Asian Conference of Geometric Topology(KIAS(Korea),(online))
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Topics around Type 7 and 8 knots of Berge's lens space surgery2022

    • Author(s)
      山田裕一
    • Organizer
      研究集会「微分トポロジー21~デーン手術~」(立命館大学(online))
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Difficulty on divide knot presentation of Type 8 knots in Berge's lens space surgery2021

    • Author(s)
      山田裕一
    • Organizer
      研究集会「4次元トポロジー」(大阪大学(online))
    • Related Report
      2021 Annual Research Report
  • [Presentation] Instantons and Four-Manifolds 4章 CP2の錐2021

    • Author(s)
      山田 裕一
    • Organizer
      研究集会「 微分トポロジー21~インスタントンゲージ理論スクール~」
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Gabai の4次元版電球定理の証明を概説2019

    • Author(s)
      山田裕一
    • Organizer
      非公式なセミナー(早稲田大学)
    • Related Report
      2019 Research-status Report
  • [Presentation] Exceptional Dehn surgeries along certain two-component links related to 4-manifolds2018

    • Author(s)
      Yuichi YAMADA
    • Organizer
      "Four Dimensional Topology", Department of Mathematics, Osaka City University (Sumiyoshi-ku, Osaka)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sporadic knots of lens space surgery2018

    • Author(s)
      山田 裕一
    • Organizer
      研究集会「瀬戸内結び目セミナー」 大島商船高専(山口県大島郡周防大島町)
    • Related Report
      2018 Research-status Report
  • [Presentation] 4次元多様体論に現れる、いくつかの2成分絡み目に沿う例外的デーン手術の分布2018

    • Author(s)
      山田 裕一
    • Organizer
      「4次元トポロジーセミナー」 大阪大学大学院 理学研究科数学専攻(大阪府豊中市待兼山町)
    • Related Report
      2018 Research-status Report
  • [Presentation] 4-dimensional light bulb theorem by Gabai II2018

    • Author(s)
      山田 裕一
    • Organizer
      研究集会「 微分トポロジー19~4次元多様体に埋め込まれた曲面とその手術~」 立命館大学(東京キャンパス)(東京都千代田区 サピアタワー8F)
    • Related Report
      2018 Research-status Report
  • [Presentation] Real analogues of spaces of resultants and its related problems2018

    • Author(s)
      山口 耕平
    • Organizer
      RIMS共同研究(公開型)研究集会「変換群における幾何・代数・組み合わせ論」, 京都大学数理解析研究所 (京都市左京区)
    • Related Report
      2018 Research-status Report
  • [Presentation] Spaces of resultants with bounded multiplicity and its real analogues2018

    • Author(s)
      山口 耕平
    • Organizer
      研究集会「実特異点論とその応用」
    • Related Report
      2017 Research-status Report
  • [Presentation] Exceptional Dehn surgeries along the Mazur link2017

    • Author(s)
      山田 裕一
    • Organizer
      日本数学会 秋季総合分科会(山形大学)
    • Related Report
      2017 Research-status Report
  • [Presentation] Spaces of resultants of bounded multiplicity and its related problems2017

    • Author(s)
      山口 耕平
    • Organizer
      研究集会「空間の代数的・幾何的モデルとその周辺」
    • Related Report
      2017 Research-status Report
  • [Presentation] Change maker とトーラス結び目のレンズ空間手術2016

    • Author(s)
      山田裕一
    • Organizer
      研究集会「瀬戸内結び目セミナー」
    • Place of Presentation
      大島商船高専(山口県大島郡周防大島町)
    • Related Report
      2016 Research-status Report
  • [Remarks] 山田裕一のページ

    • URL

      http://www.yyyamada.e-one.uec.ac.jp/indexj.html

    • Related Report
      2021 Annual Research Report 2020 Research-status Report 2019 Research-status Report 2018 Research-status Report 2017 Research-status Report
  • [Remarks] 微分トポロジー '22 デーン手術

    • URL

      http://www.math.tsukuba.ac.jp/~tange/diftop22.html

    • Related Report
      2021 Annual Research Report
  • [Remarks] 研究集会「微分トポロジー19 ~4次元多様体に埋め込まれた曲面とその手術~」

    • URL

      http://www.math.tsukuba.ac.jp/~tange/diftop19.html

    • Related Report
      2018 Research-status Report
  • [Remarks] Differential Topology 17

    • URL

      http://www.math.tsukuba.ac.jp/~tange/diftop17e.html

    • Related Report
      2016 Research-status Report
  • [Remarks] 山田裕一のホームページ

    • URL

      http://www.yyyamada.e-one.uec.ac.jp/indexj.html

    • Related Report
      2016 Research-status Report
  • [Funded Workshop] Differential Topology'172017

    • Place of Presentation
      電気通信大学(東京都調布市)
    • Year and Date
      2017-03-28
    • Related Report
      2016 Research-status Report
  • [Funded Workshop] The 12th East Asia School of Knots and Related Topics2017

    • Place of Presentation
      東京大学大学院 数理科学研究科(東京都目黒区駒場)
    • Year and Date
      2017-02-13
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2023-01-30  

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