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Research on the intersection of a pair of homogeneous Lagrangian submanifolds and Floer homology

Research Project

Project/Area Number 24740049
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionIbaraki University (2015)
Tokyo Denki University (2012-2014)

Principal Investigator

IRIYEH HIROSHI  茨城大学, 理学部, 准教授 (30385489)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsFloerコホモロジー / ラグランジュ部分多様体 / 複素旗多様体 / 実形 / 対蹠集合 / ハミルトン体積最小性 / トポロジー / Floerホモロジー / 旗多様体 / 幾何学 / 等径超曲面 / シンプレクティック多様体
Outline of Final Research Achievements

The purpose of this research is to reveal the symplectic topological nature of
a Lagrangian submanifold with a high degree of symmetry in a symplectic manifold. There were few concrete studies concerned with this kind of Lagrangian submanifold. By using the symmetries of these spaces, in particular in the complex projective space, we obtained the results about homological rigidity of Lagrangian submanifolds, explicit calculations of Lagrangian Floer cohomology, including an application to the Hamiltonian volume minimizing problem.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (13 results)

All 2016 2015 2014 2013 Other

All Journal Article (5 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 2 results) Presentation (8 results)

  • [Journal Article] Almost all Lagrangian torus orbits in CP^n are not Hamiltonian volume minimizing2016

    • Author(s)
      Hiroshi Iriyeh, Hajime Ono
    • Journal Title

      Annals of Global Analysis and Geometry

      Volume: 49 Issue: 1 Pages: 85-96

    • DOI

      10.1007/s10455-016-9504-6

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Symplectic topology of Lagrangian submanifolds of CP^n with intermediate minimal Maslov numbers2016

    • Author(s)
      Hiroshi Iriyeh
    • Journal Title

      Advances in Geometry

      Volume: -

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Lagrangian intersection theory and Hamiltonian volume minimizing problem2014

    • Author(s)
      H. Iriyeh, T. Sakai and H. Tasaki
    • Journal Title

      Springer Proceedings in Mathematics & Statistics

      Volume: 106 Pages: 391-399

    • DOI

      10.1007/978-4-431-55215-4_35

    • ISBN
      9784431552147, 9784431552154
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] 複素旗多様体内の実旗多様体の交叉の構造2014

    • Author(s)
      入江 博、酒井高司、田崎博之
    • Journal Title

      RIMS Kokyuroku

      Volume: 1880 Pages: 100-116

    • Related Report
      2013 Research-status Report
  • [Journal Article] On the structure of the intersection of real flag manifolds in a complex flag manifold2013

    • Author(s)
      Hiroshi Iriyeh, Takashi Sakai, Hiroyuki Tasaki
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: -

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 等径超曲面のGauss像のHamiltonian non-displaceability2016

    • Author(s)
      入江 博、Hui Ma、宮岡礼子、大仁田義裕
    • Organizer
      日本数学会2016年度年会
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 複素旗多様体内の二つの実旗多様体の交叉2015

    • Author(s)
      井川 治、入江 博、奥田 隆幸、酒井 高司、田崎 博之
    • Organizer
      日本数学会2015年度年会
    • Place of Presentation
      明治大学(東京都千代田区)
    • Year and Date
      2015-03-22
    • Related Report
      2014 Research-status Report
  • [Presentation] 非Hamilton体積最小なHamilton安定Lagrangeトーラスについて2014

    • Author(s)
      入江 博、小野 肇
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] 複素旗多様体内の四元数旗多様体の交叉の構造2014

    • Author(s)
      入江 博、酒井 高司、田崎 博之
    • Organizer
      日本数学会2014年度秋季総合分科会
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Research-status Report
  • [Presentation] 複素射影空間の中間的な最小Maslov数をもつLagrange部分多様体のホモロジー的剛性

    • Author(s)
      入江 博
    • Organizer
      日本数学会
    • Place of Presentation
      愛媛大学(愛媛県)
    • Related Report
      2013 Research-status Report
  • [Presentation] Symplectic Topology of Lagrangian Submanifolds

    • Author(s)
      Hiroshi Iriyeh
    • Organizer
      NCTS Symplectic Geometry Seminar
    • Place of Presentation
      国立成功大学(台湾)
    • Related Report
      2013 Research-status Report
  • [Presentation] 複素旗多様体内の実旗多様体の交叉の構造

    • Author(s)
      入江 博、酒井高司、田崎博之
    • Organizer
      日本数学会
    • Place of Presentation
      九州大学(福岡県)
    • Related Report
      2012 Research-status Report
  • [Presentation] Lagrangian Floer homology of a pair of real forms in Hermitian symmetric spaces and its application

    • Author(s)
      Hiroshi Iriyeh
    • Organizer
      ETH Symplectic Geometry Seminar
    • Place of Presentation
      ETH(ZURICH)
    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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