Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

Details Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case

1999-09-13

arxiv.org/abs/math/9909191v1

Geom. Topol. 3 (1999), 303-330

Mathematics

Geometric Topology

28 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper13.abs.html

Scientific paper

In this article, we generalize Eberlein's Rigidity Theorem to the singular case, namely, one of the spaces is only assumed to be a CAT(0) topological manifold. As a corollary, we get that any compact irreducible but locally reducible locally symmetric space of noncompact type does not admit a nonpositively curved (in the Aleksandrov sense) piecewise Euclidean structure. Any hyperbolic manifold, on the other hand, does admit such a structure.

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