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arXiv · 1308.0663

A free product formula for the sofic dimension

Robert Graham·Mikael Pichot
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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 \[ s(G)=\h(G_1^0)s(G_1)+\h(G_2^0)s(G_2)-\h(G_3^0)s(G_3) \] where $\h$ is the normalized Haar measure on $G$.

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Robert Graham, Mikael Pichot. 2013-08-03. A free product formula for the sofic dimension. https://doi.org/10.4153/cjm-2014-019-5

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