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Symplectic geometry and contact topology for manifolds with boundary and its applications

Research Project

Project/Area Number 17F17318
Research Category

Grant-in-Aid for JSPS Fellows

Allocation TypeSingle-year Grants
Section外国
Research Field Geometry
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) BAE YEONGJIN  京都大学, 数理解析研究所, 外国人特別研究員
Project Period (FY) 2017-11-10 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2019: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2018: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2017: ¥600,000 (Direct Cost: ¥600,000)
Keywords接触多様体 / ルジャンドルグラフ / 次数付き微分代数 / 添加写像 / ルーリング不変量 / 接触ホモロジー / ルジャンドル結び目 / 接触構造 / Chekanov-Eliashberg DGA / ruling invariant / wrapped Floer theory / wrapped Floer ホモロジー
Outline of Annual Research Achievements

標準的な接触空間内の Legendre 結び目、絡み目については、回転数や TB 不変量といった古典的な不変量では区別できないものも Chekanov, Eliashberg による Legendre DGA により区別できることがある。Chekanov-Eliashberg DGA は、Legendre 部分多様体に対する接触ホモロジーを背景に組み合わせ的考察により定義された。An 氏 (IBS-CGP) との共同研究で、この構成を Legendre グラフへと拡張した。この成果は A Chekanov-Eliashberg algebra for Legendrian graphs, J. Topol. 13 (2020), 777-869 に纏められた。また、その接触ホモロジー的な解釈を模索した。
Chekanov-Eliashberg DGA には augmentation (添加写像) と言う概念があり、augmentation (の同値類のなす) 空間も重要な研究対象である。また、Chekanov, Pushkar による ruling も重要な不変量である。Bae 氏は An 氏、Kalman 氏 (東工大) との共同研究で、augmentation の存在と ruling の存在の同値性など Legendre 結び目、絡み目で知られている結果を Legendre graph の場合に拡張することに成功した。これらの成果を Ruling invariants for Legendrian graphs (An, Bae, Kalman), Su 氏 (ENS, Paris) とのAugmentations and ruling polynomials for Legendrian graphs (An, Bae, Su) に纏めた。

Research Progress Status

令和元年度が最終年度であるため、記入しない。

Strategy for Future Research Activity

令和元年度が最終年度であるため、記入しない。

Report

(3 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report
  • 2017 Annual Research Report
  • Research Products

    (14 results)

All 2020 2019 2018 Other

All Int'l Joint Research (4 results) Journal Article (3 results) (of which Int'l Joint Research: 2 results,  Peer Reviewed: 3 results) Presentation (7 results) (of which Int'l Joint Research: 3 results,  Invited: 7 results)

  • [Int'l Joint Research] IBS Center for Geometry and Physics(韓国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Ecole Normale Superieure(フランス)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] IBS Center for Geometry and Physics(韓国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] IBS Center for Geometry and Physics(韓国)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A Chekanov-Eliashberg algebra for Legendrian graphs2020

    • Author(s)
      B. An and Y. Bae
    • Journal Title

      Journal of Topology

      Volume: 13 Issue: 2 Pages: 777-869

    • DOI

      10.1112/topo.12138

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodic orbits of virtually contact structures2020

    • Author(s)
      Youngjin Bae, Kevin Wiegand, Kai Zehmisch
    • Journal Title

      Journal of Topology and Analysis

      Volume: 印刷中

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Legendrian singular links and singular connected sums2018

    • Author(s)
      Byung Hee An, Youngjin Bae, Seonhwa Kim
    • Journal Title

      Journal of Symplectic Geometry

      Volume: 16 Issue: 4 Pages: 885-930

    • DOI

      10.4310/jsg.2018.v16.n4.a1

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Exact Lagrangian fillings of Legendrian torus knots2019

    • Author(s)
      Youngjin Bae
    • Organizer
      seminar at University of Giessen, Germany
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Exact Lagrangian fillings of Legendrian torus knots2019

    • Author(s)
      Youngjin Bae
    • Organizer
      seminar at Seoul National University
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Symplectic embeddings and symplectic capacities2018

    • Author(s)
      Youngjin Bae
    • Organizer
      NIMS Research School on symplectic embeddings, systolic inequalities and celestial mechanics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A Chekanov-Eliashberg algebra for Legendrian graphs2018

    • Author(s)
      Youngjin Bae
    • Organizer
      Pacific Rim Complex Symplectic Geometry Conference
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A Chekanov-Eliashberg algebra for Legendrian graphs, I & II2018

    • Author(s)
      Youngjin Bae
    • Organizer
      KMS-DMV joint meeting
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A Chekanov-Eliashberg algebra for Legendrian graphs2018

    • Author(s)
      Yeongjin Bae (Youngjin Bae)
    • Organizer
      接触構造、特異点、微分方程式及びその周辺
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Floer homology for knot complements2018

    • Author(s)
      Yeongjin Bae (Youngjin Bae)
    • Organizer
      名古屋大学幾何学セミナー
    • Related Report
      2017 Annual Research Report
    • Invited

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Published: 2017-11-13   Modified: 2024-03-26  

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