Hyperlinear approximations to amenable groups come from sofic approximations

2021/10/06 by Burton, Peter
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2110.03076

Abstract

We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. This translates to a quantitative relationship between Hilbert-Schmidt and permutation stability for approximate homomorphisms which appropriately separate the elements of the group.

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