Nonintegrable tangent distributions and topology of manifolds

• Project/Area Number: 21540058
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Hokkaido 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: ¥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.

Research Products

• [Journal Article] Relative local equivalence of Engel structures (2012)
  • 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
  • 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
• [Journal Article] A certain surgery construction of contact 3-mianifolds (2011)
  • Author(s): Jiro Adachi
  • Journal Title: 数理解析研究所講究録 Volume: 1,764 Pages: 139-148
• [Journal Article] Global Stability of special multi-flags (2010)
  • Author(s): Jiro Adachi
  • Journal Title: Israel J. Math. Volume: 179 Pages: 29-56
  • Peer Reviewed
• [Journal Article] Global stability of special multi-flags (2010)
  • Author(s): Jiro ADACHI
  • Journal Title: Israel Journal of Mathematics Volume: 179 Pages: 29-56
  • 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
• [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
• [Journal Article] Global stability of special multi-flags
  • Author(s): 足立二郎
  • Journal Title: Israel Journal of Mathematics (to appear)
  • 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
• [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
• [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
• [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
• [Presentation] Contact Round surgery and symplectic round handlebodies (2011)
  • 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
• [Presentation] Contact round surgery and symplectic round handlebodies (2011)
  • 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
• [Presentation] Generalizations of the Gray theorem (2011)
  • 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
• [Presentation] Generalizations of the Gray theorem (2011)
  • Author(s): Jiro Adachi
  • Organizer: Israeli-Polish Mathematical Meeting
  • Place of Presentation: Lodz, Poland
  • Year and Date: 2011-09-13
• [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
• [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
• [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
• [Presentation] A certain surgery construction of contact 3-manifolds (2010)
  • 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
• [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
• [Presentation] Round surgery and contact structures (2010)
  • 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
• [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
• [Presentation] A certain new surgery construction of contact 3-manifolds (2010)
  • 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
• [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
• [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
• [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
• [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
• [Presentation] Engel geometry from a flexible viewpoint (2009)
  • Author(s): Jiro Adachi
  • Organizer: Polish-Japanese Singularity theory working days
  • Place of Presentation: Kazimierz Dolny, Poland
  • Year and Date: 2009-07-18
• [Presentation] Engel geometry from a flexible viewpoint (2009)
  • Author(s): 足立二郎
  • Organizer: Geometric Singularity Theory
  • Place of Presentation: Kazimierz Dolny, Poland
  • Year and Date: 2009-07-18