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Some new rigidity results for stable orbit equivalence

Published online by Cambridge University Press:  19 September 2008

Scot Adams
Scot Adams
Affiliation:
Department of Mathematics, Vincent Hall 206 Church St, SE University of Minnesota Minneapolis, MN 55455, USA
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Abstract

Broadly speaking, we prove that an action of a group with very little commutativity cannot be stably orbit equivalent to an action of a group with enough commutativity, assuming both actions are free and finite measure preserving. For example, one group may be SL2(ℝ) and the other a group with infinite discrete center (e.g., the universal cover of SL2(ℝ)); I believe this is the first rigidity result of this type for a pair of simpleLie groups both of split rank one. Another example: one group may be any nonelementary word hyperbolic group, the other any group with infinite discrete center.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 15 , Issue 2 , April 1995 , pp. 209 - 219
Copyright
Copyright © Cambridge University Press 1995

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