C*-rigidity of bounded geometry metric spaces
Operator Algebras
2025-03-10 v1
Abstract
We prove that uniformly locally finite metric spaces with isomorphic Roe algebras must be coarsely equivalent. As an application, we also prove that the outer automorphism group of the Roe algebra of a metric space of bounded geometry is canonically isomorphic to the group of coarse equivalences of the space up to closeness.
Keywords
Cite
@article{arxiv.2501.03128,
title = {C*-rigidity of bounded geometry metric spaces},
author = {Diego Martínez and Federico Vigolo},
journal= {arXiv preprint arXiv:2501.03128},
year = {2025}
}
Comments
An extract of [arxiv:2403.13624], proving a particular case of its main theorem in the special case of bounded geometry metric spaces. 15 pages