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Analysis of deformation space of 3-dimensional cone-hyperbolic structures using fundamental domains arising from cut loci

Research Project

Project/Area Number 20740043
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Geometry
Research InstitutionKinki University

Principal Investigator

AKIYOSHI Hirotaka  Kinki University, 理工学部, 准教授 (80397611)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords幾何学 / トポロジー
Research Abstract

The space of cone-hyperbolic structures for the 3-dimensional cone-manifold obtained as the product of the torus with a cone-point and the real line was studied in order to establish the deformation theory of 3-dimensional cone-hyperbolic structures for cone-manifolds with noncompact cone singularity. The deformation was studied by using a variant of Ford domains in the theory of Kleinian groups. A geometric parametrization for such space was established, which is conjectured to give a parametrization for certain slice of the character variety of one-holed torus defined by Tan et al. in terms of dynamics on the variety.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (4 results)

All 2009 2008

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

  • [Journal Article] Side Parameter for the Punctured Torus Groups2009

    • Author(s)
      Hirtotaka Akiyoshi
    • Journal Title

      Proceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

      Pages: 58-62

    • Related Report
      2010 Final Research Report
  • [Journal Article] Side Parameter for the Punctured Torus Groups2009

    • Author(s)
      Hirtotaka Akiyoshi
    • Journal Title

      Proceedings of the 16^<th> International Conference on Finite or Infinite Dimensional Complex Analysis and Applications

      Pages: 58-62

    • Related Report
      2009 Annual Research Report
  • [Presentation] Side parameter for the punctured torus groups2008

    • Author(s)
      秋吉宏尚
    • Organizer
      The 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Dongguk University(韓国 慶州)
    • Year and Date
      2008-07-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Side parameter for the pullctured torus groups2008

    • Author(s)
      秋吉宏尚
    • Organizer
      The 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications
    • Place of Presentation
      Dongguk University(韓国慶州)
    • Year and Date
      2008-07-29
    • Related Report
      2008 Annual Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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