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arXiv · 2101.04522

Covering dimension of Cuntz semigroups

Hannes Thiel·Eduard Vilalta
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Abstract

We introduce a notion of covering dimension for Cuntz semigroups of C*-algebras. This dimension is always bounded by the nuclear dimension of the C*-algebra, and for subhomogeneous C*-algebras both dimensions agree. Cuntz semigroups of Z-stable C*-algebras have dimension at most one. Further, the Cuntz semigroup of a simple, Z-stable C*-algebra is zero-dimensional if and only if the C*-algebra has real rank zero or is stably projectionless.

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Hannes Thiel, Eduard Vilalta. 2021-01-12. Covering dimension of Cuntz semigroups. https://arxiv.org/abs/2101.04522

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