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Overall study of topology

Research Project

Project/Area Number 19204007
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionOsaka City University

Principal Investigator

MASUDA Mikiya  Osaka City University, 大学院・理学研究科, 教授 (00143371)

Co-Investigator(Kenkyū-buntansha) MATSUMOTO Shigenori  日本大学, 理工学部, 教授 (80060143)
TSUBOI Takashi  東京大学, 大学院・数理科学研究科, 教授 (40114566)
OHSHIKA Ken'ichi  大阪大学, 大学院・数理科学研究科, 教授 (70183225)
KONO Akira  京都大学, 大学院・理学研究科, 教授 (00093237)
KOJIMA Sadayoshi  東京工業大学, 大学院・情報理工研究科, 教授 (90117705)
IZUMIYA Shuichi  北海道大学, 大学院・理学研究科, 教授 (80127422)
SAKUMA Makoto  広島大学, 大学院・理学研究科, 教授 (30178602)
FUKAYA Kenji  京都大学, 大学院・理学研究科, 教授 (30165261)
SAEKI Osamu  九州大学, 大学院・数理学研究科, 教授 (30201510)
KATO Hisao  筑波大学, 大学院・数理物質科学研究科, 教授 (70152733)
KOHNO Toshitake  東京大学, 大学院・数理科学研究科, 教授 (80144111)
KANENOBU Taizo  大阪市立大学, 大学院・理学研究科, 教授 (00152819)
MORITA Shigeyuki  東京大学, 大学院・数理科学研究科, 教授 (70011674)
NAKAI Isao  お茶の水女子大学, 理学部, 教授 (90207704)
KAWAUCHI Akio  大阪市立大学, 大学院・理学研究科, 教授 (00112524)
KAWAZUMI Nariya  東京大学, 大学院・数理科学研究科, 准教授 (30214646)
IWASE Norio  九州大学, 大学院・数理学研究科, 教授 (60213287)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥37,960,000 (Direct Cost: ¥29,200,000、Indirect Cost: ¥8,760,000)
Fiscal Year 2009: ¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2008: ¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2007: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Keywords位相幾何 / トポロジー / 多様体 / 群 / 結び目 / シンプレクティック幾何 / トーリックトポロジー
Research Abstract

In this project, we held about 40 workshops and had two researcher exchanges in topology from a wide viewpoint with the help of the cooperation researchers. Through this activity, we planned to enhance the field of topology, seek a new development and raise young researchers in topology. Concerning my research on toric topology, I worked on the cohomological rigidity problem for toric manifolds and symmetry of torus manifolds. I also gave young researchers opportunities to attend and/or give talks at conferences on topics related to toric topology.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (20 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (5 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Topologocal classification of generalized Bott towers2010

    • Author(s)
      S.Choi, M.Masuda, D.Y.Suh
    • Journal Title

      Transactions of Amer.Math.Soc. 362

      Pages: 1097-1112

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cohomological rigidity of real Bott manifolds2009

    • Author(s)
      Yoshinobu Kamishima, Mikiya Masuda
    • Journal Title

      Alg. & Geom. Topology

      Pages: 2479-2502

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant classification of 2-torus manifolds2009

    • Author(s)
      Z.Lu, M.Masuda
    • Journal Title

      Colloq.Math. 115

      Pages: 171-188

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cohomological rigidity of real Bott manifolds2009

    • Author(s)
      Y.Kamishima, M.Masuda
    • Journal Title

      Algebraic & Geometric Topology 9

      Pages: 2479-2502

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semifree circle actions, Bott towers, and quasitoric manifolds2008

    • Author(s)
      Mikiya Masuda, Taras Panov
    • Journal Title

      Sbornik Math 199

      Pages: 1201-1223

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant cohomology distinguishes toric manifolds2008

    • Author(s)
      Mikiya Masuda
    • Journal Title

      Adv. Math 218

      Pages: 2005-2012

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification problems of toric manifolds via topology2008

    • Author(s)
      Mikiya Masuda, Dong Youp Suh
    • Journal Title

      Contemp. Math 460

      Pages: 273-286

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification problems of toric manifolds via topology2008

    • Author(s)
      M. Masuda, D. Y. Suh
    • Journal Title

      Contemporary Mathematics 460

      Pages: 273-286

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant cohomology distinguishes toric manifolds2008

    • Author(s)
      M. Masuda
    • Journal Title

      Advances in Mathematics 218

      Pages: 2005-2012

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semifree circle actions, Bott towers and quasitoric manifolds2008

    • Author(s)
      M Masuda, T. Panov
    • Journal Title

      Sbornik Math. 199

      Pages: 1201-1223

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Torus graphs and simplicial posets2007

    • Author(s)
      Hiroshi Maeda
    • Journal Title

      Advances in Mathematics 212

      Pages: 458-483

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Samelson products of $\rm SO(3)$ and applications2007

    • Author(s)
      Kmiyama Yasuhiko
    • Journal Title

      Glasgow Mathematical Journal 49

      Pages: 405-409

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Equivariant cohomology distinguishes toric manifolds

    • Author(s)
      Mikiya Masuda
    • Journal Title

      Advances in Mathematics (掲載確定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Symmetry of torus manifolds2009

    • Author(s)
      M.Masuda
    • Organizer
      BRATISLAVA TOPOLOGY SYMPOSIUM "Group Actions and Homogeneous Spaces"
    • Place of Presentation
      Bratislava(スロバキア)
    • Year and Date
      2009-09-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Classification problems on toric manifolds via cohomology2008

    • Author(s)
      Mikiya Masuda
    • Organizer
      New Horizons in Toric Topology
    • Place of Presentation
      Manchster
    • Year and Date
      2008-07-20
    • Related Report
      2009 Final Research Report
  • [Presentation] Classification problems on toric manifolds via topology2008

    • Author(s)
      M. Masuda
    • Organizer
      New Horizons on Toric Topology
    • Place of Presentation
      Manchester Univ. (イギリス)
    • Year and Date
      2008-07-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Topological Toric Theory2008

    • Author(s)
      Mikiya Masuda
    • Organizer
      International Conference on Differential Equations and Topology dedicated to the Centennial Anniversary of L.S. Pontryagin
    • Place of Presentation
      Moscow
    • Year and Date
      2008-06-20
    • Related Report
      2009 Final Research Report
  • [Presentation] トーリックトポロジー2008

    • Author(s)
      Mikiya Masuda
    • Organizer
      研究集会「トーリック多様体の理論の展開と応刷」
    • Place of Presentation
      東北大学
    • Related Report
      2007 Annual Research Report
  • [Book] Toric Topology (Contemporary Mathematics 460)2008

    • Author(s)
      Harada, Karshon, Masuda, Panov
    • Total Pages
      401
    • Publisher
      American Mathematical Society
    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.ms.u-tokyo.ac.jp/~takahiko/summer_school07/summer_school.html

    • Related Report
      2007 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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