A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras
Operator Algebras
2025-05-12 v2
Abstract
We show that two simple, separable, nuclear and -stable -algebras are isomorphic if they are trace-preservingly homotopy equivalent. This result does not assume the UCT and can be viewed as a tracial stably projectionless analog of the homotopy rigidity theorem for Kirchberg algebras.
Cite
@article{arxiv.2505.04857,
title = {A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras},
author = {Jorge Castillejos and Baukje Debets and Gabor Szabo},
journal= {arXiv preprint arXiv:2505.04857},
year = {2025}
}
Comments
13 pages