2000/04/10 by Dave Witte, Witte, Dave, Robert J. Zimmer +1
Mathematics · #22F10 (Primary) 28D15 #37A20 (Secondary) #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.DS #math.RT #msc:22F10 #msc:28D15 #msc:37A20
paper · pdf · doi:10.48550/arxiv.math/0004057
29 pages. Latex2e file requires style files from Kluwer Academic Publishers: http://www.wkap.nl/kapis/stylefiles/kluwer.zip
arxiv created 2000/04/10 · openalex publication_date 2000/04/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.