Boundaries of deformation spaces of Kleinian groups

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540083
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Nagoya University
• Principal Investigator: ITO Kentaro 名古屋大学, 多元数理科学研究科, 准教授 (00324400)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 双曲幾何 / クライン群

Outline of Final Research Achievements

I studied boundary behavior of deformation spaces of Kleinan groups. Especially, I studied the deformation space of the once-punctured torus group and made clear that how linear slices of traces close to 2 converge or not converge to the linear slice of trace 2 (Maskit slice). This is obtained from Bromberg's theory of non-local connectivity of the deformation space by using the trace coordinates. I also studied the deformation space of the twice-punctured torus groups. In addition, I started a research of distributions of totally geodesic planes in hyperbolic 3-manifolds. This corresponds to the study of actions of Kleinan groups on the 3-dimensional de-Sitter space.

Free Research Field

幾何学