Rigidity results for certain 3-dimensional singular spaces and their fundamental groups
Group Theory
2007-05-23 v1 Differential Geometry
Metric Geometry
Abstract
In this paper, we introduce a particularly nice family of locally CAT(-1) spaces, which we call hyperbolic P-manifolds. For a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometric rigidity for these spaces.
Cite
@article{arxiv.math/0409586,
title = {Rigidity results for certain 3-dimensional singular spaces and their fundamental groups},
author = {J. -F. Lafont},
journal= {arXiv preprint arXiv:math/0409586},
year = {2007}
}
Comments
26 pages, 3 figures; to appear in Geom. Dedicata