Actions of Semisimple Lie Groups on Circle Bundles |
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| Authors: | Dave Witte Robert J Zimmer |
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| Institution: | (1) Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078, U.S.A.;(2) Department of Mathematics, University of Chicago, Chicago, IL, 60637, U.S.A. |
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| Abstract: | Suppose G is a connected, simple, real Lie group with
-rank(G)  2, M is an ergodic G-space with invariant probability measure  , and  : G × M  Homeo(
) is a Borel cocycle. We use an argument of É. Ghys to show that there is a G-invariant probability measure  on the skew product M ×
, such that the projection of to M is . Furthermore, if (G × M)  Diff1(
), then can be taken to be equivalent to ×  , where is Lebesgue measure on
; therefore, is cohomologous to a cocycle with values in the isometry group of
. |
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| Keywords: | group action semisimple Lie group circle bundle measurable cocycle S-arithmatic group Kazhdan's property T |
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