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arXiv · 1901.09441

$\mathrm{K}$-theory and homotopies of twists on ample groupoids

Christian Bönicke
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Abstract

This paper investigates the $\mathrm{K}$-theory of twisted groupoid $\mathrm{C}^*$-algebras. It is shown that a homotopy of twists on an ample groupoid satisfying the Baum-Connes conjecture with coefficients gives rise to an isomorphism between the $\mathrm{K}$-theory groups of the respective twisted groupoid $\mathrm{C}^*$-algebras. The results are also interpreted in an inverse semigroup setting and applied to generalized Renault-Deaconu groupoids and $P$-graph algebras.

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Christian Bönicke. 2019-01-27. $\mathrm{K}$-theory and homotopies of twists on ample groupoids. https://arxiv.org/abs/1901.09441

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