2010 Fiscal Year Final Research Report
Analysis of deformation space of 3-dimensional cone-hyperbolic structures using fundamental domains arising from cut loci
| Project/Area Number |
20740043
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kinki University |
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Principal Investigator |
AKIYOSHI Hirotaka Kinki University, 理工学部, 准教授 (80397611)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 幾何学 / トポロジー |
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| 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.
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Research Products
(2 results)
