location:  Publications → journals → CJM
Abstract view

# A Free Product Formula for the Sofic Dimension

Published:2014-10-10
Printed: Apr 2015
• Robert Graham,
McGill University
• Mikael Pichot,
McGill University
 Format: LaTeX MathJax PDF

## Abstract

It is proved that if $G=G_1*_{G_3}G_2$ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $G_3$, then the sofic dimension $s(G)$ satisfies the equality $s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3)$ where $\mathfrak{h}$ is the normalized Haar measure on $G$.
 Keywords: sofic groups, dynamical systems, orbit equivalence, free entropy
 MSC Classifications: 20E06 - Free products, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations

 top of page | contact us | privacy | site map |