Relative Property (T) Actions and Trivial Outer Automorphism Groups
Abstract
We show that every non-amenable free product of groups admits free ergodic probability measure preserving actions which have relative property (T) in the sense of S.-Popa \cite[Def. 4.1]{Pop06}. There are uncountably many such actions up to orbit equivalence and von Neumann equivalence, and they may be chosen to be conjugate to any prescribed action when restricted to the free factors. We exhibit also, for every non-amenable free product of groups, free ergodic probability measure preserving actions whose associated equivalence relation has trivial outer automorphisms group. This gives in particular the first examples of such actions for the free group on generators.
Keywords
Cite
@article{arxiv.0804.0358,
title = {Relative Property (T) Actions and Trivial Outer Automorphism Groups},
author = {Damien Gaboriau},
journal= {arXiv preprint arXiv:0804.0358},
year = {2010}
}
Comments
Improvement in the presentation of the replacement trick. Introduction of compressions for non-ergodic equivalence relations