English

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 X3X^3 a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X3X^3 are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometric rigidity for these spaces.

Keywords

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