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Relations between invariants of low-dimensional manifolds and their geometric structures

Research Project

Project/Area Number 24540076
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKyoto University

Principal Investigator

Ue Masaaki  京都大学, 理学(系)研究科(研究院), 教授 (80134443)

Co-Investigator(Kenkyū-buntansha) Tsuyoshi Kato  京都大学, 理学研究科, 教授 (20273427)
Michihiko Fujii  京都大学, 理学研究科, 准教授 (60254231)
Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords低次元トポロジー / 3次元多様体 / 4次元多様体 / Seiberg-Witten理論 / Heegaard Floerホモロジー / ザイフェルト多様体 / ホモロジーコボルディズム / 4次元多様体 / 3次元多様体 / エータ不変量
Outline of Final Research Achievements

Ue studied invariants of 3-manifolds originated from the Seiberg-Witten and the Heegaard Floer homology theory. In particular in case of Seifert rational homology 3-spheres,which consist of special classes among 3-manifolds, he proved the mu-bar invariant (which is combinatorially defined) is represented by some combinations of analytically defined eta invariants under certain conditions using the Seiberg-Witten theory. He announced the above results at the conferences in Japan and overseas from 2012 to 2015 and completed the preprint (which is prepared to submit). He also continued to write a textbook on 4-manifolds, which started several years ago, including the latest achievements. He is trying to make the textbook in complete form within a year.

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

(5 results)

All 2015 2014 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results) Presentation (4 results) (of which Invited: 3 results)

  • [Journal Article] Computation of the spherical growth series of finitely generated groups and monoids by using automata2015

    • Author(s)
      Michihiko Fujii
    • Journal Title

      Handbook of group actions, Vol. II, Adv. Lect. Math.

      Volume: 32 Pages: 479-521

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed
  • [Presentation] ザイフェルトホモロジー3球面のmu-bar不変量,エータ不変量とd不変量について2015

    • Author(s)
      上 正明
    • Organizer
      微分トポロジー15
    • Place of Presentation
      京都大学大学院理学研究科数学教室
    • Year and Date
      2015-03-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The mu-bar invariants and the eta invariants for Seifert homology 3-spheres2014

    • Author(s)
      上 正明
    • Organizer
      研究集会「多様体のトポロジーの展望」
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2014-11-29
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The mu-bar invariants and the eta invariants for Seifert rational homology 3-spheres

    • Author(s)
      上 正明
    • Organizer
      Workshop and Conference on the Topology and Invariants of Smooth 4-Manifolds
    • Place of Presentation
      University of Minnesota
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] The mu-bar invariants, the eta invariants and Ozsvath-Szabo's correction terms for Seifert rational homology 3-spheres

    • Author(s)
      上 正明
    • Organizer
      研究集会「4次元トポロジー」
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report

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

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