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Gauge theory and localization

Research Project

Project/Area Number 24340011
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypePartial Multi-year Fund
Section一般
Research Field Geometry
Research InstitutionThe University of Tokyo

Principal Investigator

Furuta Mikio  東京大学, 数理(科)学研究科(研究院), 教授 (50181459)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥11,180,000 (Direct Cost: ¥8,600,000、Indirect Cost: ¥2,580,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2012: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsトポロジー / 4次元多様体 / ゲージ理論 / 幾何学 / 微分トポロジー / 多様体上の解析
Outline of Final Research Achievements

We investigated gauge theory on 4-manifolds using mathematical approach. While final outputs in physics are usually supposed to be some numbers, such as probabilities, it is known that we can construct some richer structures as outputs in the mathematical approach to gauge theory. Our goal is to find new properties of 4-manifolds using such rich structures. A major result of our research is a relation between the "signature" of a 4-manifold and the structure of the 3-manifold (Floer K gruop) which appears as its boundary.

Report

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

    (22 results)

All 2016 2015 2014 2013 2012 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (17 results) (of which Int'l Joint Research: 6 results,  Invited: 16 results)

  • [Journal Article] Equivariant version of Rochlin-type congruences2014

    • Author(s)
      M. Furua and Y. Kametani
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 66 Issue: 1 Pages: 205-221

    • DOI

      10.2969/jmsj/06610205

    • NAID

      130003394353

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Torus Fibrations and Localization of Index II2014

    • Author(s)
      H. Fujita, M.Furuta and T.Yoshida
    • Journal Title

      Communications in Mathematical Physics

      Volume: 326 Issue: 3 Pages: 585-633

    • DOI

      10.1007/s00220-014-1890-7

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Torus Fibrations and Localization of Index III2014

    • Author(s)
      H. Fujita, M.Furuta and T.Yoshida
    • Journal Title

      Communications in Mathematical Physics

      Volume: 327 Issue: 3 Pages: 665-689

    • DOI

      10.1007/s00220-014-2039-4

    • Related Report
      2014 Annual Research Report 2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant version of Rochlin-type congruences2013

    • Author(s)
      M. Furuta and Y. Kametani
    • Journal Title

      Journal of The Mathematical Society of Japan

      Volume: (in press)

    • NAID

      130003394353

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Pin"-(2) -monopole equations and intersection forms with local coefficients of four-manifolds2013

    • Author(s)
      N. Nakamura
    • Journal Title

      Mathematische Annalen

      Volume: (online) Issue: 3 Pages: 915-939

    • DOI

      10.1007/s00208-013-0924-3

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Presentation] Topological Invariants and Partial Differential Equations2016

    • Author(s)
      古田幹雄
    • Organizer
      The AIMR International Symposium 2016
    • Place of Presentation
      東北大学AIMR
    • Year and Date
      2016-02-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Seiberg-Witten不変量と有限次元近似」2016

    • Author(s)
      古田幹雄
    • Organizer
      , 第 11 回代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学
    • Year and Date
      2016-02-15
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] An introduction to Seiberg-Witten equations2016

    • Author(s)
      古田幹雄
    • Organizer
      Berkeley-Tokyo Winter School "Geometry, Topology and Representation Theory
    • Place of Presentation
      米国 UC Berkeley
    • Year and Date
      2016-02-08
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Yang-Mills theory / Seiberg-Witten theory2015

    • Author(s)
      古田幹雄
    • Organizer
      2015 SNU 4-Manifolds Workshop
    • Place of Presentation
      韓国 Oak Valley
    • Year and Date
      2015-12-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] トポロジカル不変量と偏微分方程式2015

    • Author(s)
      古田幹雄
    • Organizer
      第1回 トポロジーが紡ぐ物質科学のフロンティア 領域研究会
    • Place of Presentation
      京都大学
    • Year and Date
      2015-12-11
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] トポロジカル絶縁体 -バルク・エッジ対応の数学2015

    • Author(s)
      古田幹雄
    • Organizer
      日本女子大学理学セミナー
    • Place of Presentation
      日本女子大学
    • Year and Date
      2015-10-30
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 10/8-type inequalities and TQFT”,,, October 2015(豪)2015

    • Author(s)
      古田幹雄
    • Organizer
      IGA/AMSI Workshop “Australia-Japan Geometry, Analysis and their Applications”
    • Place of Presentation
      オーストラリア Adelaide University
    • Year and Date
      2015-10-20
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Bott periodicity and the bulk-edge correspondence", International Workshop :2015

    • Author(s)
      古田幹雄
    • Organizer
      Mathematical Approach to Topological Phases in Spintronics,
    • Place of Presentation
      東北大学
    • Year and Date
      2015-10-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 10/8-type inequalities and TQFT" ,2015

    • Author(s)
      古田幹雄
    • Organizer
      Trends in Modern Geometry & the 10th Pacific Rim Complex Geometry Conference
    • Place of Presentation
      東京大学
    • Year and Date
      2015-07-27
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] バルクエッジ対応とBott周期性2014

    • Author(s)
      古田幹雄
    • Organizer
      幾何学セミナー・トポロジー金曜セミナー
    • Place of Presentation
      九州大学 大学院数理学研究院
    • Year and Date
      2014-12-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] The perturbation of the Seiberg-Witten equations revisited2014

    • Author(s)
      M. Furuta
    • Organizer
      Workshop on Topology and Invariants of 4-Manifolds
    • Place of Presentation
      SCGP, 米国
    • Year and Date
      2014-08-24
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] ゲージ理論のいくつかの側面2014

    • Author(s)
      古田幹雄
    • Organizer
      第61回トポロジーシンポジウム
    • Place of Presentation
      東北大学
    • Year and Date
      2014-07-28
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] An introduction to gauge theories2012

    • Author(s)
      M. Furuta
    • Organizer
      SNU-KIAS Topology Winter School
    • Place of Presentation
      韓国 Muju(招待講演)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Dirac operators on spin 4-manifolds and mod 2 index

    • Author(s)
      M. Furuta
    • Organizer
      Topological Phases in Spintronics
    • Place of Presentation
      AIMR 東北大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] A TQFT for spin 4-manifolds associated with Pin(2)-equivariant Seiberg-Witten Floer K-group

    • Author(s)
      M. Furuta
    • Organizer
      the Fourth Tsinghua-Sanya International Mathematics Forum
    • Place of Presentation
      Sanya, (中国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Two variants of the 10/8 inequality

    • Author(s)
      M. Furuta
    • Organizer
      Workshop and Conference on the Topology and Invariants of Smooth 4-Manifolds
    • Place of Presentation
      Minneapolis, (米国)
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] Seiberg-Witten Floer K cohomology and a 10/8-type inequality for spin 4-manifolds with boundaries

    • Author(s)
      M. Furuta
    • Organizer
      Geometry and topology of smooth 4-manifolds
    • Place of Presentation
      Max Planck Institute for Mathematics, Bonn (ドイツ)
    • Related Report
      2013 Annual Research Report
    • Invited

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Published: 2012-04-24   Modified: 2019-07-29  

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