Flexible stability and nonsoficity

Abstract

A sofic group G G is said to be flexibly stable if every sofic approximation to G 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 P S L d ( Z ) \mathrm {PSL}_d(\mathbb {Z}) is flexibly stable for some d ≥ 5 d \geq 5 , then there exists a group which is not sofic.