Flexible stability and nonsoficity

Bowen, Lewis; Burton, Peter

doi:10.1090/tran/8047

Flexible stability and nonsoficity
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by Lewis Bowen and Peter Burton PDF

Trans. Amer. Math. Soc. 373 (2020), 4469-4481 Request permission

Abstract:

A sofic group $G$ is said to be flexibly stable if every sofic approximation to $G$ can be 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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