Higher homotopy groups of Cuntz classes

Andrew S. Toms

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arXiv · 2210.14371

Higher homotopy groups of Cuntz classes

Andrew S. Toms

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Abstract

Let $A$ be a unital simple separable exact C$^*$-algebra which is approximately divisible and of real rank zero. We prove that the set of positive elements in $A$ with a fixed non-compact Cuntz class has vanishing homotopy groups. Combined with work of S. Zhang for the case of compact elements, this gives a complete calculation of the homotopy groups of Cuntz classes for these algebras. Examples covered include approximately finite-dimensional (AF) algebras and irrational noncommutative tori.

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BibTeX RIS

Andrew S. Toms. 2022-10-25. Higher homotopy groups of Cuntz classes. https://arxiv.org/abs/2210.14371

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