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STRONG JORDAN SEPARATION AND APPLICATIONS TO RIGIDITY

Published online by Cambridge University Press:  16 June 2006

JEAN-FRANÇOIS LAFONT
JEAN-FRANÇOIS LAFONT
Affiliation:
Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174, USAjlafont@math.ohio-state.edu
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Abstract

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

Keywords

20F67 (primary)53C2457N3557N50 (secondary)
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 3 , June 2006 , pp. 681 - 700
Copyright
The London Mathematical Society 2006

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