Strong Jordan separation and applications to rigidity

Details Strong Jordan separation and applications to rigidity Strong Jordan separation and applications to rigidity

2004-10-21

arxiv.org/abs/math/0410476v2

J. London Math. Soc. 73 (2006), pgs. 681-700

Mathematics

Geometric Topology

25 pages; shorter proofs of Lemmas 2.4, 2.5, minor typos corrected, added references

Scientific paper

We prove that simple, thick hyperbolic P-manifolds of dimension >2 exhibit Mostow rigidity. We also prove a quasi-isometry rigidity result for the fundamental groups of simple, thick hyperbolic P-manifolds of dimension >2. The key tool in the proofs of these rigidity results is a strong form of the Jordan separation theorem, for maps from S^n to S^{n+1} which are not necessarily injective.

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