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Contact topology from the view point of round surgery

Research Project

Project/Area Number 25400077
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

Adachi Jiro  北海道大学, 理学研究院, 理学研究院研究員 (20374184)

Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords接触構造 / ラウンド手術 / 過旋性 / シンプレクティック充填可能性
Outline of Final Research Achievements

Contact structure is an important geometric structure, that is related to classical mechanics and optics. Apart from such a historical background, the study of contact structure as a pure geometric structure has been remarkably developed recently from the view point of differential topology.
In this research project, I applied the "round surgery" method to contact manifolds, that was used for other studies. As a result, I extended the studies which had been mainly done on contact structures of the first order on 3-dimensional manifolds to the cases of higher-dimension and higher-order. It is expected that various studies will be developed by using this method.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (27 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (7 results) Journal Article (2 results) (of which Acknowledgement Compliant: 2 results,  Peer Reviewed: 1 results) Presentation (17 results) (of which Int'l Joint Research: 4 results,  Invited: 6 results) Funded Workshop (1 results)

  • [Int'l Joint Research] University of Texas/Massachusetts Institute of Technology/University of Georgia(米国)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Warsaw(Poland)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] Technion(Israel)

    • Related Report
      2017 Annual Research Report
  • [Int'l Joint Research] University of Warsaw(Poland)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Technion(イスラエル)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] University of Warsaw(ポーランド)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Massachusetts Institute of Technology(米国)

    • Related Report
      2015 Research-status Report
  • [Journal Article] 接触ラウンド手術と Lutz 捻りについて2015

    • Author(s)
      足立二郎
    • Journal Title

      数理解析研究所講究録

      Volume: 1948 Pages: 65-76

    • NAID

      110009921492

    • Related Report
      2015 Research-status Report
    • Acknowledgement Compliant
  • [Journal Article] Contact round surgery and symplectic round handlebodies2014

    • Author(s)
      Jiro Adachi
    • Journal Title

      International Journal of Mathematics

      Volume: 25 Issue: 05 Pages: 1450050-1450050

    • DOI

      10.1142/s0129167x14500505

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Contact structures and round surgeries2018

    • Author(s)
      Jiro ADACHI
    • Organizer
      Singularity theory and its applications
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 接触構造とその特性葉層について2017

    • Author(s)
      足立 二郎
    • Organizer
      微分幾何学と特異点論の応用
    • Related Report
      2017 Annual Research Report
  • [Presentation] Flexibility and round surgery of contact structures2017

    • Author(s)
      Jiro ADACHI
    • Organizer
      Geometric and Algebraic Singularity Theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 接触構造とその特性葉層について2017

    • Author(s)
      足立 二郎
    • Organizer
      葉層構造と微分同相群2017
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 高次元の接触構造のねじれと過旋性について2017

    • Author(s)
      足立 二郎
    • Organizer
      高次元の接触構造のねじれと過旋性について” 接触構造、特異点、微分方程式及びその周辺
    • Place of Presentation
      金沢大学サテライト・プラザ (石川県・金沢市)
    • Related Report
      2016 Research-status Report
  • [Presentation] コアがトーラスの plastikstufe について2016

    • Author(s)
      足立 二郎
    • Organizer
      第 39 回トポロジーセミナー
    • Place of Presentation
      ホテル伊東ガーデン(静岡県・伊東市)
    • Year and Date
      2016-03-23
    • Related Report
      2015 Research-status Report
  • [Presentation] 接触構造の過旋性のある特徴付けについて2016

    • Author(s)
      足立 二郎
    • Organizer
      トポロジー・特異点論とその応用
    • Place of Presentation
      青山学院大学 (神奈川県・相模原市)
    • Related Report
      2016 Research-status Report
  • [Presentation] トーラスが芯の plastikstufe と過旋性と高次元 Lutz 捩り2016

    • Author(s)
      足立 二郎
    • Organizer
      葉層構造と微分同相群 2016 研究集会
    • Place of Presentation
      東京大学玉原国際セミナーハウス (群馬県・沼田市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Contact round surgery and its application2015

    • Author(s)
      Jiro Adachi
    • Organizer
      Geometric singularity theory
    • Place of Presentation
      ワルシャワ(ポーランド)
    • Year and Date
      2015-09-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 接触ラウンド手術の応用をめざして2015

    • Author(s)
      足立 二郎
    • Organizer
      尾鷲微分トポロジー 2015
    • Place of Presentation
      尾鷲市中央公民館(三重県・尾鷲市)
    • Year and Date
      2015-08-11
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Round surgery and contact structure2015

    • Author(s)
      Jiro Adachi
    • Organizer
      Singularities in Generic Geometry and its Applications
    • Place of Presentation
      京都大学数理解析研究所(京都府・京都市)
    • Year and Date
      2015-06-08
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 接触ラウンド手術と接触構造のねじれについて2015

    • Author(s)
      足立 二郎
    • Organizer
      接触構造、特異点、微分方程式及びその周辺
    • Place of Presentation
      旭川市ときわ市民ホール(北海道)
    • Year and Date
      2015-01-23
    • Related Report
      2014 Research-status Report
  • [Presentation] 接触ラウンド手術と Lutz 捻りについて2014

    • Author(s)
      足立 二郎
    • Organizer
      可微分写像の特異点論とその応用
    • Place of Presentation
      京都大学数理解析研究所(京都市)
    • Year and Date
      2014-12-03
    • Related Report
      2014 Research-status Report
  • [Presentation] 接触ラウンド手術と Lutz ねじり2014

    • Author(s)
      足立 二郎
    • Organizer
      葉層構造と微分同相群 2014
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県)
    • Year and Date
      2014-10-23
    • Related Report
      2014 Research-status Report
  • [Presentation] Contact round surgery and its application2014

    • Author(s)
      Jiro Adachi
    • Organizer
      Workshop on Singularities, Geometry, Topology and Related Topics
    • Place of Presentation
      東北師範大学(中国)
    • Year and Date
      2014-09-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] ラウンド手術の接触構造への影響について

    • Author(s)
      足立 二郎
    • Organizer
      位相幾何・微分幾何と特異点論の関わり
    • Place of Presentation
      弘前大学(弘前市)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 接触円形手術とその応用について

    • Author(s)
      足立 二郎
    • Organizer
      尾鷲微分トポロジー2013
    • Place of Presentation
      尾鷲市立中央公民館(三重県)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Funded Workshop] Geometric and Algebraic Singularity Theory2017

    • Related Report
      2017 Annual Research Report

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Published: 2014-07-25   Modified: 2022-06-07  

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