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2016 $K$-theory and homotopies of 2-cocycles on group bundles
Elizabeth Gillaspy
Rocky Mountain J. Math. 46(4): 1207-1229 (2016). DOI: 10.1216/RMJ-2016-46-4-1207

Abstract

This paper continues the author's program of investigating the question of when a homotopy of 2-cocycles $\Omega = \{\omega _t\}_{t \in [0,1]}$ on a locally compact Hausdorff groupoid $\mathcal{G} $ induces an isomorphism of the $K$-theory groups of the twisted groupoid $C^*$-algebras: \[ K_*(C^*(\mathcal{G} , \omega _0)) \cong K_*(C^*(\mathcal{G} , \omega _1)). \] Building on our earlier work in \cite {eag-kgraph, transf-gps}, we show that, if $\pi : \mathcal{G} \to M$ is a locally trivial bundle of amenable groups over a locally compact Hausdorff space $M$, a homotopy $\Omega = \{\omega _t\}_{t \in [0,1]}$ of 2-cocycles on $\mathcal{G} $ gives rise to an isomorphism: \[ K_*(C^*(\mathcal{G} , \omega _0)) \cong K_*(C^*(\mathcal{G} , \omega _1)). \]

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Elizabeth Gillaspy. "$K$-theory and homotopies of 2-cocycles on group bundles." Rocky Mountain J. Math. 46 (4) 1207 - 1229, 2016. https://doi.org/10.1216/RMJ-2016-46-4-1207

Information

Published: 2016
First available in Project Euclid: 19 October 2016

zbMATH: 1357.46065
MathSciNet: MR3563179
Digital Object Identifier: 10.1216/RMJ-2016-46-4-1207

Subjects:
Primary: 46L05, 46L80

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

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Vol.46 • No. 4 • 2016
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