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 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
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)