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Research on homotopy algebraic models for geometry

Research Project

Project/Area Number 22740033
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionChiba University

Principal Investigator

KAJIURA Hiroshige  千葉大学, 大学院・理学研究科, 准教授 (30447891)

Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords幾何学 / トポロジー / 代数学 / 数理物理 / 素粒子論
Research Abstract

We showed that A∞-enhancements of triangulated categories are not unique in general by constructing such an example.
On the other hand, for the homological mirror symmetry between symplectic manifolds and complex manifolds both of which are described by torus fibrations, we constructed noncommutative deformations of the complex manifolds, define deformations of symplectic manifolds as theire mirror partners, and discussed that homological mirror symmectry between these pairs of deformations hold true.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (6 results)

All 2013 2011 2010

All Journal Article (5 results) (of which Peer Reviewed: 4 results) Book (1 results)

  • [Journal Article] On A ∞-enhancements for triangulated categories2013

    • Author(s)
      Hiroshige Kajiura
    • Journal Title

      Journal of Pure and Applied algebra

      Volume: 217 Pages: 1476-1503

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On A∞-enhancements for triangulated categories2013

    • Author(s)
      Hiroshige Kajiura
    • Journal Title

      Journal of Pure and Applied Algebra

      Volume: 217 Issue: 8 Pages: 1476-1503

    • DOI

      10.1016/j.jpaa.2012.11.006

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Structure of Open-Closed String Field Theory and Its Applications2011

    • Author(s)
      Hiroshige Kajiura
    • Journal Title

      Progress of theoretical physics supplement

      Volume: 188 Pages: 106-115

    • NAID

      110008670859

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Journal Article] Homologicalperturbation theory and homological mirror symmetry2011

    • Author(s)
      Hiroshige Kajiura
    • Journal Title

      Progress inMathematics

      Volume: 287 Pages: 201-226

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Homological perturbation theory and homological mirror symmetry2011

    • Author(s)
      Hiroshige Kajiura
    • Journal Title

      Progress in Mathematics

      Volume: 287 Pages: 201-226

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Book] 数物系のための圏論2010

    • Author(s)
      梶浦宏成
    • Total Pages
      206
    • Publisher
      サイエンス社
    • Related Report
      2012 Final Research Report 2010 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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