Rigidity results for certain 3-dimensional singular spaces and their fundamental groups

Details Rigidity results for certain 3-dimensional singular spaces and their fundamental groups Rigidity results for certain 3-dimensional singular spaces and their fundamental groups

2004-09-29

arxiv.org/abs/math/0409586v1

Geom. Dedicata, 109 (2004), pgs. 197-219.

Mathematics

Group Theory

26 pages, 3 figures; to appear in Geom. Dedicata

Scientific paper

In this paper, we introduce a particularly nice family of locally CAT(-1) spaces, which we call hyperbolic P-manifolds. For $X^3$ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of $X^3$ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometric rigidity for these spaces.

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