Year: 2026
Type: preprint
Abstract: Let $A$ be a unital, simple, separable, and pure $C^*$-algebra. We prove that, for every $a\in A_+$, the set of positive elements in $A$ having the same Cuntz class as $a$ is path-connected. This may be viewed as a generalization to positive elements of the classical homotopy theory of projection classes and extends a line of results on the topology of constant Cuntz classes that previously required stronger regularity hypotheses to the class of pure $C^*$-algebras, which notably contains all selfless algebras.
Source: arXiv (Cornell University)
Authors: Ouseph, Chrisil, Toms, Andrew S.
Institution: Purdue University West Lafayette
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221146416