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
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kinki University |
|---|
Principal Investigator |
AKIYOSHI Hirotaka Kinki University, 理工学部, 准教授 (80397611)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| 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.
|
