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

Abstract

This paper investigates the $\mathrm{K}$-theory of twisted groupoid ${\mathrm{C}}^{\ast }$-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 ${\mathrm{C}}^{\ast }$-algebras. The results are also interpreted in an inverse semigroup setting and applied to generalized Renault-Deaconu groupoids and $P$-graph algebras.

arXiv comment23 pages, minor corrections. Proposition 4.2 added. This version will appear in the Journal of Noncommutative Geometry

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Cited by in corpus (2)

• Twisted Steinberg algebras
• A Going-Down principle for ample groupoids and the Baum-Connes conjecture