Geometric property (T) for box spaces and sofic approximations
Group Theory
2025-11-21 v1 Metric Geometry
Operator Algebras
Abstract
We prove that every sofic approximation of a property (T) group is approximately isomorphic to one having geometric property (T), and more generally, a box space of graphs which has boundary geometric property (T) is approximately isomorphic to one having geometric property (T). We also prove that a sequence of bounded degree graphs is approximately isomorphic to a disjoint union of expanders if and only if the Laplacian has spectral gap in the ultraproduct. Finally, we prove a local geometric criterion for geometric property (T) in the spirit of \.{Z}uk's criterion for property (T) for groups.
Cite
@article{arxiv.2511.16515,
title = {Geometric property (T) for box spaces and sofic approximations},
author = {Vadim Alekseev and Stefan Drigalla},
journal= {arXiv preprint arXiv:2511.16515},
year = {2025}
}
Comments
42 pages