Flexible stability and nonsoficity

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 $d\ge 5$ then there exists a group which is not sofic.

Improvements made based on referee's comments