Actions of semisimple Lie groups on circle bundles
Dynamical Systems
2007-05-23 v1 Representation Theory
Abstract
Suppose 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.
Keywords
Cite
@article{arxiv.math/0004057,
title = {Actions of semisimple Lie groups on circle bundles},
author = {Dave Witte and Robert J. Zimmer},
journal= {arXiv preprint arXiv:math/0004057},
year = {2007}
}
Comments
29 pages. Latex2e file requires style files from Kluwer Academic Publishers: http://www.wkap.nl/kapis/stylefiles/kluwer.zip