A measure-conjugacy invariant for free group actions
Dynamical Systems
2008-10-27 v2 Probability
Abstract
This paper introduces a new measure-conjugacy invariant for actions of free groups. Using this invariant, it is shown that two Bernoulli shifts over a finitely generated free group are measurably conjugate if and only if their base measures have the same entropy. This answers a question of Ornstein and Weiss.
Cite
@article{arxiv.0802.4294,
title = {A measure-conjugacy invariant for free group actions},
author = {Lewis Bowen},
journal= {arXiv preprint arXiv:0802.4294},
year = {2008}
}
Comments
The proofs in this version are slightly simpler than in the previous version. Also, the last 3 sections have been removed. I intend to write up the main results of those sections in a separate paper