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Homotopy theoretic study of Floer theory and its applications

Research Project

Project/Area Number 16K17590
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Geometry
Research InstitutionKyushu University

Principal Investigator

Sasahira Hirofumi  九州大学, 数理学研究院, 准教授 (30466825)

Project Period (FY) 2016-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsFloer理論 / Seiberg-Witten理論 / ホモトピー論 / トポロジー / ゲージ理論 / Seiberg-Witten-Floer理論 / 安定ホモトピー
Outline of Final Research Achievements

In the study of 3 and 4-manifolds, Floer theory plays an important role. Using Floer theory, many invariants have been defined. So far, Floer homology is mainly used. However a homotopy refinement of Floer homology, called Floer stable homotopy type, has been studied recently. I have studied Floer stable homotopy type in Seiberg-Witten theory. As an application, I constructed a gluing formula for the stable homotopy Seiberg-Witten invariants for 4-manifolds.

Academic Significance and Societal Importance of the Research Achievements

Floerホモロジーはこれまで、低次元トポロジーやシンプレクティック幾何学において様々な重要な応用を生み出してきた。本研究では、Seiberg-Witten理論においてFloerホモロジーの精密化であるFloer安定ホモトピー型を研究した。本研究では、Floerホモトピー型の基礎的な研究が中心であったが、いくつかの応用も得た。今後、さらなる応用が生み出せる状況にある。さらに、Seiberg-Witten理論において研究を行ったが、将来、インスタントンFloer理論やシンプレクティックFloer理論への拡張も研究されていくと考えられる。

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (16 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (2 results) Journal Article (1 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 1 results) Presentation (12 results) (of which Int'l Joint Research: 5 results,  Invited: 11 results) Funded Workshop (1 results)

  • [Int'l Joint Research] MIT(米国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] MIT(米国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Unfolded Seiberg-Witten Floer spectra, I: Definition and invariance2018

    • Author(s)
      T. Khandhawit, J. Lin, H. Sasahira
    • Journal Title

      Geometry and Topology

      Volume: 22 Issue: 4 Pages: 2027-2114

    • DOI

      10.2140/gt.2018.22.2027

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] The Seiberg-Witten equations and topology2019

    • Author(s)
      笹平 裕史
    • Organizer
      OIST Geometry and Dynamics seminar
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Twisted Donaldson invariants2018

    • Author(s)
      笹平 裕史
    • Organizer
      Spring operator algebra program
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Seiberg-Witten方程式とトポロジー2018

    • Author(s)
      笹平 裕史
    • Organizer
      九州大学談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] ゲージ理論と非可換幾何学2018

    • Author(s)
      笹平 裕史
    • Organizer
      Year-End workshop on geometry and related topics in Kagoshima
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Analytic construction of spectral section2018

    • Author(s)
      笹平 裕史
    • Organizer
      Gauge theory in Fukuoka
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Seiberg-Witten方程式とその応用2018

    • Author(s)
      笹平 裕史
    • Organizer
      日本数学会 幾何学分科会 特別講演
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Twisted Donaldson invariants2017

    • Author(s)
      笹平 裕史
    • Organizer
      Advances in non commutative geometry
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ゲージ理論の低次元トポロジーへの応用2017

    • Author(s)
      笹平 裕史
    • Organizer
      京都大学数学教室 談話会
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Unfolded Seiberg-Witten-Floer spectra2017

    • Author(s)
      笹平 裕史
    • Organizer
      幾何学セミナー
    • Place of Presentation
      九州大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Unfolded Seiberg-Witten-Floer spectra2017

    • Author(s)
      笹平 裕史
    • Organizer
      Australia-Japan Geometry, Analysis and their Applications
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Seiberg-Witten-Floer安定ホモトピー型2016

    • Author(s)
      笹平 裕史
    • Organizer
      関西ゲージ理論セミナー
    • Place of Presentation
      京都大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 有理ホモロジー3球面の Seiberg-Witten-Floer 安定ホモトピー型2016

    • Author(s)
      笹平 裕史
    • Organizer
      Seiberg-Witten-Floer stable homotopy type 勉強会
    • Place of Presentation
      東京大学
    • Related Report
      2016 Research-status Report
    • Invited
  • [Funded Workshop] Gauge theory in Fukuoka2018

    • Related Report
      2017 Research-status Report

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Published: 2016-04-21   Modified: 2022-02-21  

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