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2010 Fiscal Year Final Research Report

Existence problem and deformation of compact Clifford-Klein forms

Research Project

  • PDF
Project/Area Number 20740033
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionTokyo Institute of Technology

Principal Investigator

YOSHINO Taro  Tokyo Institute of Technology, 大学院・理工学研究科, 助教 (20447890)

Project Period (FY) 2008 – 2010
Keywords非リーマン等質空間 / 不連続群 / Clifford-Klein形 / 位相的ブローアップ / 変形空間 / 非ハウスドルフ空間 / Lipsman予想の反例
Research Abstract

At first, I had planed to calculate deformation spaces of Clifford-Klein forms. However, I found that such deformation spaces are non-Hausdorff in many cases, and it is not easy to get an intuition of the deformation space.
In order to understand such non-Hausdorff spaces, I have introduced a method topological blow-up'. This method is similar to the blow-up for algebraic varieties. Applying this method for a non-Hausdorff space, we obtain a Hausdorff space. This Hausdorff space has much information about the topology of the original non-Hausdorff space. Especially, if we apply it for deformation spaces of Clifford-Klein forms, we can obtain complete information on the topology of the deformation space from the blow-upped spaces.

  • Research Products

    (4 results)

All 2010 Other

All Journal Article (1 results) Presentation (2 results) Remarks (1 results)

  • [Journal Article] Topological blow-up and discontinuous groups2010

    • Author(s)
      Taro Yoshino
    • Journal Title

      Mathematicsches Forschungsinstitut Oberwolfach 25

      Pages: 34-37

  • [Presentation] Topological blow-up and discontinuous groups2010

    • Author(s)
      Taro Yoshino
    • Organizer
      Representation Theory and Harmonic Analysis
    • Place of Presentation
      ドイツ
    • Year and Date
      20101114-20101120
  • [Presentation] Topological blow-up2010

    • Author(s)
      Taro Yoshino
    • Organizer
      Analysis, Geometry and Group Representations for Homogeneous Spaces
    • Place of Presentation
      オランダ
    • Year and Date
      2010-11-25
  • [Remarks] ホームページ等

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Published: 2012-02-13   Modified: 2016-04-21  

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