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Nonintegrable tangent distributions and topology of manifolds

Research Project

Project/Area Number 21540058
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

ADACHI Jiro  北海道大学, 大学院・理学研究院, 非常勤講師 (20374184)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords円形ハンドル / 接触構造 / エンゲル構造 / シンプレクティック構造 / 円形手術 / 相対的局所安定性
Research Abstract

I studied some properties of the so-called contact structures. A contact structure is a completely nonintegrable hyperplane field on a so-called manifold. I introduced a new notion of contact round surgery by constructing symplectic round handle. It is expected to be applied to the higher dimensional and higher order contact geometry.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (30 results)

All 2012 2011 2010 2009 Other

All Journal Article (8 results) (of which Peer Reviewed: 4 results) Presentation (22 results)

  • [Journal Article] Relative local equivalence of Engel structures2012

    • Author(s)
      Jiro Adachi
    • Journal Title

      Math. Z.

      Volume: (Online First 版) Issue: 3-4 Pages: 711-733

    • DOI

      10.1007/s00209-012-1026-8

    • Related Report
      2011 Annual Research Report 2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 円形手術と接触構造2011

    • Author(s)
      Jiro Adachi
    • Journal Title

      数理解析研究所講究録

      Volume: 1764 Pages: 139-148

    • Related Report
      2011 Final Research Report
  • [Journal Article] A certain surgery construction of contact 3-mianifolds2011

    • Author(s)
      Jiro Adachi
    • Journal Title

      数理解析研究所講究録

      Volume: 1,764 Pages: 139-148

    • Related Report
      2011 Annual Research Report
  • [Journal Article] Global Stability of special multi-flags2010

    • Author(s)
      Jiro Adachi
    • Journal Title

      Israel J. Math.

      Volume: 179 Pages: 29-56

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global stability of special multi-flags2010

    • Author(s)
      Jiro ADACHI
    • Journal Title

      Israel Journal of Mathematics

      Volume: 179 Pages: 29-56

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 4次元多様体の手術とEngel構造2009

    • Author(s)
      Jiro Adachi
    • Journal Title

      数理解析研究所講究録

      Volume: 1664 Pages: 105-116

    • Related Report
      2011 Final Research Report
  • [Journal Article] 4次元多様体の手術とEngel構造2009

    • Author(s)
      足立二郎
    • Journal Title

      数理解析研究所講究録 1664

      Pages: 105-116

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Global stability of special multi-flags

    • Author(s)
      足立二郎
    • Journal Title

      Israel Journal of Mathematics (to appear)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 相対的なDarboux型の定理について2012

    • Author(s)
      足立二郎
    • Organizer
      第35回トポロジーセミナー(旧・伊豆セミナー)
    • Place of Presentation
      千葉県館山市
    • Year and Date
      2012-03-18
    • Related Report
      2011 Final Research Report
  • [Presentation] 相対的Darboux型定理について2012

    • Author(s)
      足立二郎
    • Organizer
      第35回トポロジーセミナー(旧・伊豆セミナー)
    • Place of Presentation
      たてやま夕日海岸ホテル(千葉県)(招待講演)
    • Year and Date
      2012-03-18
    • Related Report
      2011 Annual Research Report
  • [Presentation] 円形手術から見た接触構造2012

    • Author(s)
      足立二郎
    • Organizer
      接触構造・特異点・微分方程式およびその周辺
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2012-01-19
    • Related Report
      2011 Final Research Report
  • [Presentation] 円形手術から見た接触構造2012

    • Author(s)
      足立二郎
    • Organizer
      接触構造・特異点・微分方程式およびその周辺
    • Place of Presentation
      鹿児島大学(鹿児島市)(招待講演)
    • Year and Date
      2012-01-19
    • Related Report
      2011 Annual Research Report
  • [Presentation] Contact Round surgery and symplectic round handlebodies2011

    • Author(s)
      Jiro Adachi
    • Organizer
      多様体の平面場と微分同相群2011
    • Place of Presentation
      東京大学玉原国際セミナーハウス(沼田市)(招待講演)
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] Contact round surgery and symplectic round handlebodies2011

    • Author(s)
      Jiro Adachi
    • Organizer
      多様体の平面場と微分同相群2011
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2011-11-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Generalizations of the Gray theorem2011

    • Author(s)
      Jiro Adachi
    • Organizer
      Israeli-Polish Mathematical Meeting
    • Place of Presentation
      ウッヂ大学(ポーランド)
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] Generalizations of the Gray theorem2011

    • Author(s)
      Jiro Adachi
    • Organizer
      Israeli-Polish Mathematical Meeting
    • Place of Presentation
      Lodz, Poland
    • Year and Date
      2011-09-13
    • Related Report
      2011 Final Research Report
  • [Presentation] 接触円形手術と斜交円形把手体2011

    • Author(s)
      足立二郎
    • Organizer
      特異点論とその応用
    • Place of Presentation
      大分工業高等専門学校
    • Year and Date
      2011-06-02
    • Related Report
      2011 Final Research Report
  • [Presentation] 接触円形手術と斜交円形把手体2011

    • Author(s)
      足立二郎
    • Organizer
      特異点論とその応用
    • Place of Presentation
      大分工業高等専門学校(大分市)(招待講演)
    • Year and Date
      2011-06-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] 接触円形手術とシンプレクティック円形ハンドル体2011

    • Author(s)
      足立二郎
    • Organizer
      特異点論セミナー
    • Place of Presentation
      北海道大学
    • Year and Date
      2011-03-11
    • Related Report
      2010 Annual Research Report
  • [Presentation] A certain surgery construction of contact 3-manifolds2010

    • Author(s)
      Jiro ADACHI
    • Organizer
      Geometry on Real Closed Field and its Application to Singularity Theory
    • Place of Presentation
      京都大学数理解析研究所 招待講演
    • Year and Date
      2010-12-06
    • Related Report
      2010 Annual Research Report
  • [Presentation] 円形手術と接触構造2010

    • Author(s)
      Jiro Adachi
    • Organizer
      実閉体上の幾何と特異点論への応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Round surgery and contact structures2010

    • Author(s)
      Jiro Adachi
    • Organizer
      葉層構造と微分同相群2010
    • Place of Presentation
      東京大学玉原国際セミナーハウス
    • Year and Date
      2010-10-28
    • Related Report
      2011 Final Research Report
  • [Presentation] Round surgery and contact structures 招待講演2010

    • Author(s)
      Jiro ADACHI
    • Organizer
      Foliations and Groups of Diffeomorphisms 2010
    • Place of Presentation
      東京大学玉原国際セミナーハウス 招待講演
    • Year and Date
      2010-10-28
    • Related Report
      2010 Annual Research Report
  • [Presentation] A certain new surgery construction of contact 3-manifolds2010

    • Author(s)
      Jiro Adachi
    • Organizer
      特異点と多様体の幾何学
    • Place of Presentation
      山形大学
    • Year and Date
      2010-09-17
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] 円形手術と接触構造2010

    • Author(s)
      足立二郎
    • Organizer
      空間認識のための特異点論
    • Place of Presentation
      三重県伊勢市観光文化会館
    • Year and Date
      2010-06-04
    • Related Report
      2011 Final Research Report
  • [Presentation] 円形手術と接触構造2010

    • Author(s)
      足立二郎
    • Organizer
      空間認識のための特異点論
    • Place of Presentation
      伊勢市観光文化会館 招待講演
    • Year and Date
      2010-06-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] 接触構造と円形手術2010

    • 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
      北海道洞爺湖文化センター
    • Year and Date
      2010-01-29
    • Related Report
      2011 Final Research Report
  • [Presentation] 接触構造と円形手術2010

    • 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
      洞爺湖文化センター,北海道
    • Year and Date
      2010-01-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] Engel geometry from a flexible viewpoint2009

    • Author(s)
      Jiro Adachi
    • Organizer
      Polish-Japanese Singularity theory working days
    • Place of Presentation
      Kazimierz Dolny, Poland
    • Year and Date
      2009-07-18
    • Related Report
      2011 Final Research Report
  • [Presentation] Engel geometry from a flexible viewpoint2009

    • Author(s)
      足立二郎
    • Organizer
      Geometric Singularity Theory
    • Place of Presentation
      Kazimierz Dolny, Poland
    • Year and Date
      2009-07-18
    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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