Sofic dimension for discrete measured groupoids
Dynamical Systems
2012-11-13 v2 Group Theory
Abstract
For discrete measured groupoids preserving a probability measure we introduce a notion of sofic dimension that measures the asymptotic growth of the number of sofic approximations on larger and larger finite sets. In the case of groups we give a formula for free products with amalgamation over an amenable subgroup. We also prove a free product formula for measure-preserving actions.
Cite
@article{arxiv.1111.2842,
title = {Sofic dimension for discrete measured groupoids},
author = {Ken Dykema and David Kerr and Mikael Pichot},
journal= {arXiv preprint arXiv:1111.2842},
year = {2012}
}
Comments
38 pages, minor changes and corrections