A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras

Jorge Castillejos; Baukje Debets; Gabor Szabo

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arXiv · 2505.04857

A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras

Jorge Castillejos·Baukje Debets·Gabor Szabo

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Abstract

We show that two simple, separable, nuclear and $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-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.

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Jorge Castillejos, Baukje Debets, Gabor Szabo. 2025-05-07. A homotopy rigidity theorem for $\mathcal{Z}_0$-stable $\mathrm{C}^\ast$-algebras. https://arxiv.org/abs/2505.04857

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