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2023 Fiscal Year Annual Research Report

Studies on Floer theory and symplectic, contact structures

Research Project

Project/Area Number 19H00636
Research InstitutionKyoto University

Principal Investigator

小野 薫  京都大学, 数理解析研究所, 教授 (20204232)

Co-Investigator(Kenkyū-buntansha) 石川 剛郎  北海道大学, 理学研究院, 名誉教授 (50176161)
枡田 幹也  大阪公立大学, 大学院理学研究科, 特任教授 (00143371)
入江 慶  京都大学, 数理解析研究所, 准教授 (90645467)
三松 佳彦  中央大学, 理工学部, 教授 (70190725)
赤穂 まなぶ  東京都立大学, 理学研究科, 准教授 (30332935)
秦泉寺 雅夫  岡山大学, 環境生命自然科学学域, 教授 (20322795)
石川 卓  京都大学, 数理解析研究所, 助教 (70845742)
松下 大介  北海道大学, 理学研究院, 准教授 (90333591)
Project Period (FY) 2019-04-01 – 2024-03-31
KeywordsFloer 理論 / シンプレクティック構造 / 接触構造 / 正則曲線 / シンプレクティク orbifold
Outline of Annual Research Achievements

シンプレクティック orbifold 上のラグランジュ Floer 理論の構成に必要な dihedral twisted sector 上の局所系の考察と、境界付き正則写像の moduli を用いて filter 付き A-無限大構造を構成する際の符号の問題を扱った。それは複数のラグランジュ部分多様体が clean intersection で交わっている時の A-無限大構造の構成の時の符号の問題に帰着されるが、de Rham 複体を用いた場合にそれを詳細に書き下した Sing convention for A-infinity operations in Bott-Morse case としてまとめた。また、全体の理論の鍵となる dihedral twisted sector を中心にした Twisted sectors in Lagrangian Floer theory on symplectic orbifolds を B. Chen, B. Wang との共著として公表した。共同研究者の B. Chen, B. Wang 両氏を含む海外の研究者とも交流進み、議論が円滑にできるようになったことで、得られた研究成果の本論文の作成に進める状況になった。

Research Progress Status

令和5年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和5年度が最終年度であるため、記入しない。

  • Research Products

    (14 results)

All 2024 2023 Other

All Int'l Joint Research (5 results) Journal Article (6 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 6 results,  Open Access: 1 results) Presentation (3 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results)

  • [Int'l Joint Research] Australian National University(オーストラリア)

    • Country Name
      AUSTRALIA
    • Counterpart Institution
      Australian National University
  • [Int'l Joint Research] Sichuan University(中国)

    • Country Name
      CHINA
    • Counterpart Institution
      Sichuan University
  • [Int'l Joint Research] Czech Academy of Science(チェコ)

    • Country Name
      CZECH
    • Counterpart Institution
      Czech Academy of Science
  • [Int'l Joint Research] Institute for Basic Science, CGP(韓国)

    • Country Name
      KOREA (REP. OF KOREA)
    • Counterpart Institution
      Institute for Basic Science, CGP
  • [Int'l Joint Research] Simons Center for Geometry and Physics(米国)

    • Country Name
      U.S.A.
    • Counterpart Institution
      Simons Center for Geometry and Physics
  • [Journal Article] Twisted Sectors for Lagrangian Floer Theory on Symplectic Orbifolds2024

    • Author(s)
      Chen Bohui、Sichuan University, P.R. China、Ono Kaoru、Wang Bai-Ling、Kyoto University, Japan、The National Australian University, Australia
    • Journal Title

      Symmetry, Integrability and Geometry: Methods and Applications

      Volume: 20 Pages: -

    • DOI

      10.3842/SIGMA.2024.011

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Construction of Kuranishi structures on the moduli spaces of pseudo-holomorphic disks: II2024

    • Author(s)
      Fukaya Kenji、Oh Yong-Geun、Ohta Hiroshi、Ono Kaoru
    • Journal Title

      Advances in Mathematics

      Volume: 442 Pages: 109561~109561

    • DOI

      10.1016/j.aim.2024.109561

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Unique toric structure on a Fano Bott manifold2023

    • Author(s)
      Cho Yunhyung、Lee Eunjeong、Masuda Mikiya、Park Seonjeong
    • Journal Title

      Journal of Symplectic Geometry

      Volume: 21 Pages: 439~462

    • DOI

      10.4310/JSG.2023.v21.n3.a1

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Unicellular LLT polynomials and twins of regular semisimple Hessenberg varieties2023

    • Author(s)
      Masuda Mikiya、Sato Takashi
    • Journal Title

      International Mathematics Research Notices

      Volume: 2024 Pages: 964~996

    • DOI

      10.1093/imrn/rnac359

    • Peer Reviewed
  • [Journal Article] Singularities of parallels to tangent developable surfaces2023

    • Author(s)
      Ishikawa Goo
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 75 Pages: 233-249

    • DOI

      10.2748/tmj.20211220

    • Peer Reviewed
  • [Journal Article] Geometrical proof of generalized mirror transformation of projective hypersurfaces2023

    • Author(s)
      Jinzenji Masao
    • Journal Title

      International Journal of Mathematics

      Volume: 34 Pages: -

    • DOI

      10.1142/S0129167X23500064

    • Peer Reviewed / Open Access
  • [Presentation] Twisted sectors in Lagrangian Floer theory on symplectic orbifolds2024

    • Author(s)
      Kaoru Ono
    • Organizer
      Topology of 4-manifolds and related topics, Ocean Suite Hotel, Jeju
    • Int'l Joint Research / Invited
  • [Presentation] Orbifold Lagrangian Floer theory2023

    • Author(s)
      Kaoru Ono
    • Organizer
      International Workshop on Gromov-Witten theory, Sen-Yat sun University
    • Int'l Joint Research / Invited
  • [Presentation] On Floer-Novikov cohomology2023

    • Author(s)
      Kaoru Ono
    • Organizer
      Conference on Gauged Symplectic Invariants and Related Topics, Guangzhou Yingbin Hotel
    • Int'l Joint Research / Invited

URL: 

Published: 2024-12-25  

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