Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T11:15:51.941Z Has data issue: false hasContentIssue false

SOME COMPUTATIONS OF 1-COHOMOLOGY GROUPS AND CONSTRUCTION OF NON-ORBIT-EQUIVALENT ACTIONS

Published online by Cambridge University Press:  02 March 2006

Sorin Popa
Affiliation:
Mathematics Department, University of California, Los Angeles, CA 90095-155505, USA ([email protected])

Abstract

For each group $G$ having an infinite normal subgroup with the relative property (T) (e.g. $G=H\times K$, with $H$ infinite with property (T) and $K$ arbitrary) and each countable abelian group $\varLambda$ we construct free ergodic measure-preserving actions $\sigma_\varLambda$ of $G$ on the probability space such that the first cohomology group of $\sigma_\varLambda$, $\ssm{H}^1(\sigma_\varLambda,G)$, is equal to $\text{Char}(G)\times\varLambda$. We deduce that $G$ has uncountably many non-stably orbit-equivalent actions. We also calculate 1-cohomology groups and show existence of ‘many’ non-stably orbit-equivalent actions for free products of groups as above.

Type
Research Article
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)