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arXiv · 2412.12366

Contractible Cuntz classes in $Z$-stable C$^*$-algebras

Chrisil Ouseph·Andrew S. Toms
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Abstract

Let $A$ be a unital, simple and Z-stable C$^*$-algebra. We show that the set of positive elements in $A$ (resp. $A \otimes K$) belonging to a fixed non-compact Cuntz class is contractible as a topological subspace of $A$ (resp. $A \otimes K$). In light of earlier work by Zhang, Jiang and Hua in the compact case, we deduce a complete calculation of the homotopy groups of Cuntz classes for these algebras.

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Chrisil Ouseph, Andrew S. Toms. 2024-12-16. Contractible Cuntz classes in $Z$-stable C$^*$-algebras. https://arxiv.org/abs/2412.12366

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