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arXiv · 1906.02172

Flexible stability and nonsoficity

Lewis Bowen·Peter Burton
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Abstract

A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can converted to a sequence of disjoint unions of Schreier graphs by modifying an asymptotically vanishing proportion of edges. We establish that if $\mathrm{PSL}_d(\mathbb{Z})$ is flexibly stable for some $d \geq 5$ then there exists a group which is not sofic.

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Lewis Bowen, Peter Burton. 2019-09-27. Flexible stability and nonsoficity. https://arxiv.org/abs/1906.02172

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