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 such a metric space is canonically isomorphic to the group of coarse equivalences of the space up to closeness.
@article{PMIHES_2025__141__333_0,
author = {Mart{\'\i}nez, Diego and Vigolo, Federico},
title = {$C^\ast$-rigidity of bounded geometry metric spaces},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {333--348},
year = {2025},
publisher = {Springer International Publishing},
address = {Cham},
volume = {141},
doi = {10.1007/s10240-025-00155-3},
zbl = {08054052},
language = {en},
url = {https://www.numdam.org/articles/10.1007/s10240-025-00155-3/}
}
TY - JOUR AU - Martínez, Diego AU - Vigolo, Federico TI - $C^\ast$-rigidity of bounded geometry metric spaces JO - Publications Mathématiques de l'IHÉS PY - 2025 SP - 333 EP - 348 VL - 141 PB - Springer International Publishing PP - Cham UR - https://www.numdam.org/articles/10.1007/s10240-025-00155-3/ DO - 10.1007/s10240-025-00155-3 LA - en ID - PMIHES_2025__141__333_0 ER -
%0 Journal Article %A Martínez, Diego %A Vigolo, Federico %T $C^\ast$-rigidity of bounded geometry metric spaces %J Publications Mathématiques de l'IHÉS %D 2025 %P 333-348 %V 141 %I Springer International Publishing %C Cham %U https://www.numdam.org/articles/10.1007/s10240-025-00155-3/ %R 10.1007/s10240-025-00155-3 %G en %F PMIHES_2025__141__333_0
Martínez, Diego; Vigolo, Federico. $C^\ast$-rigidity of bounded geometry metric spaces. Publications Mathématiques de l'IHÉS, Tome 141 (2025), pp. 333-348. doi: 10.1007/s10240-025-00155-3
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