On sofic approximations of Property (T) groups

TL;DR

This paper proves Bowen's conjecture that sequences of finite graphs approximating Property (T) groups are essentially unions of expander graphs, characterized via the Markov operator, advancing understanding of graph limits and group properties.

Contribution

It establishes that graph sequences converging to Property (T) groups are unions of expanders, confirming Bowen's conjecture and providing a characterization through the Markov operator.

Findings

Sequences approximating Property (T) groups are unions of expanders.

Characterization of such graph sequences via the Markov operator.

Confirmation of Bowen's conjecture.

Abstract

We prove Bowen's conjecture that every sequence of finite graphs that locally converges to the Cayley graph of a countably infinite group with Kazhdan Property (T) is essentially a vertex-disjoint union of expander graphs. We characterize graph sequences that are essentially a vertex-disjoint union of expander graphs in terms of the Markov operator.