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

2004/09/29 by J. -F. Lafont
Mathematics · #math.GR #math.DG #math.MG #msc:20F65 #msc:20F67

paper · pdf

published as Geom. Dedicata, 109 (2004), pgs. 197-219. · 26 pages, 3 figures; to appear in Geom. Dedicata

arxiv created 2004/09/29 · arxiv updated 2009/12/01

Abstract

In this paper, we introduce a particularly nice family of locally CAT(-1) spaces, which we call hyperbolic P-manifolds. For X³ a simple, thick hyperbolic P-manifold of dimension 3, we show that certain subsets of the boundary at infinity of the universal cover of X³ are characterized topologically. Straightforward consequences include a version of Mostow rigidity, as well as quasi-isometric rigidity for these spaces.

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