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Geometric research of 2-vector fields

Research Project

Project/Area Number 20540059
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

MIKAMI Kentaro  Akita University, 工学資源学研究科, 教授 (70006592)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsポアソン / スカウテン括弧 / 同変コホモロジー / ゲルファント / クリフォード代数 / スカウテン括弧積 / コホモロジー / 同変 / ゲルファント・フックス / 自明表現 / 一般複素構造 / ポアソン構造 / ゲルファント・フックスコホモロジー / 群不変コホモロジー / ポアソンコホモロジー群 / 幾何学 / 一般化複素構造
Research Abstract

The Schouten bracket is a main tool in Poisson geometry and there are several trials of understanding of meaning of the Schouten bracket. Using some idea of generalized complex geometry, we investigated the essence of the Schouten bracket in the framework of Clifford algebra. Also, we have gotten complete understanding of difference of our Schouten bracket and the other bracket in I. Vaissman's book "Lectures on the geometry of Poisson manifolds"(Birkhauser). Concerning to Gel'fand-Kalinin-Fuks cohomology of formal Hamiltonian vector fields on symplectic 2-plane, we prepared programs of Maple which is a computer software of symbol calculus and also several computers, and made a success in getting more information of Gel'fand-Kalini-Fuks cohomology until weight 18 comparing D.Kotschick and S.Morita's work "The Gel'fand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations".

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (7 results)

All 2010 2009 2008

All Presentation (7 results)

  • [Presentation] Leaf invariants, Foliations and group of diffeomorphisms 20102010

    • Author(s)
      三上健太郎
    • Organizer
      東京大学玉原国際セミナーハウス
    • Place of Presentation
      群馬県沼田市
    • Year and Date
      2010-10-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Leaf invariants2010

    • Author(s)
      三上健太郎
    • Organizer
      Foliations and Group of diffeomorphisms 2010
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県沼田市)
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] 水谷先生とポアソン構造2010

    • Author(s)
      三上健太郎
    • Organizer
      水谷先生退職記念講演会
    • Place of Presentation
      埼玉大学(さいたま市)
    • Year and Date
      2010-03-05
    • Related Report
      2010 Final Research Report
  • [Presentation] 水谷先生とポアソン構造2010

    • Author(s)
      三上健太郎
    • Organizer
      水谷先生退職記念講演会
    • Place of Presentation
      埼玉大学
    • Year and Date
      2010-03-05
    • Related Report
      2009 Annual Research Report
  • [Presentation] Unimodular Lie algebras in Poisson Geometry2009

    • Author(s)
      三上健太郎
    • Organizer
      シンプレクティック幾何学とその周辺(幾何学分科会研究集会)
    • Place of Presentation
      岐阜経済大学(岐阜県大垣市)
    • Year and Date
      2009-11-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Unimodular Lie algebras in Poisson Geometry2009

    • Author(s)
      三上健太郎
    • Organizer
      シンプレクティック幾何学とその周辺
    • Place of Presentation
      岐阜経済大学
    • Year and Date
      2009-11-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Symplectic and/or Poisson Geometries in Vector Bundles2008

    • Author(s)
      三上健太郎
    • Organizer
      新潟微分幾何学研究集会2008
    • Place of Presentation
      新潟大学五十嵐構内
    • Year and Date
      2008-11-05
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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