English

On sofic approximations of Property (T) groups

Combinatorics 2019-07-31 v5 Group Theory

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.

Keywords

Cite

@article{arxiv.1606.04471,
  title  = {On sofic approximations of Property (T) groups},
  author = {Gabor Kun},
  journal= {arXiv preprint arXiv:1606.04471},
  year   = {2019}
}

Comments

The use of different notions of expanders has been confusing in the earlier versions, where one-sided and two-sided expanders have not been distinguished (Theorem 2 in v1-v3) sufficiently. Theorem 3 and Corollary 5 deal with these separately

R2 v1 2026-06-22T14:25:15.766Z