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29 March 2024
 
  » arxiv » math.DS/0004057

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Actions of semisimple Lie groups on circle bundles
Dave Witte ; Robert J. Zimmer ;
Date 10 Apr 2000
Subject Dynamical Systems; Representation Theory MSC-class: 22F10 (Primary) 28D15, 37A20 (Secondary) | math.DS math.RT
AffiliationOklahoma State University), Robert J. Zimmer (University of Chicago
AbstractSuppose G is a connected, simple, real Lie group with real rank at least two, M is an ergodic G-space with invariant probability measure, and f is a Homeo(T)-valued Borel cocycle, where Homeo(T) denotes the group of homeomorphisms of the circle T. We use an argument of E.Ghys to show that there is a G-invariant probability measure on the skew product of M and T. Furthermore, if the image of f consists of diffeomorphisms, then there is an invariant measure that is equivalent to the product measure; therefore, f is cohomologous to a cocycle with values in the isometry group of T.
Source arXiv, math.DS/0004057
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