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Smooth cocycle rigidity for expanding maps, and an application to Mostow rigidity

Published online by Cambridge University Press:  17 June 2002

OLIVER JENKINSON
OLIVER JENKINSON
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS. e-mail: [email protected]
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Abstract

We give a variation on the proof of Mostow's rigidity theorem, for certain hyperbolic 3-manifolds. This is based on a rigidity theorem for conjugacies between piecewise-conformal expanding Markov maps. The conjugacy rigidity theorem is deduced from a Livsic cocycle rigidity theorem that we prove for smooth, compact Lie group-valued cocycles over piecewise smooth expanding Markov maps.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 132 , Issue 3 , May 2002 , pp. 439 - 452
Copyright
2002 Cambridge Philosophical Society

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