K-theory and homotopies of 2-cocycles on group bundles

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Abstract

This paper continues the author's program of investigating the question of when a homotopy of 2-cocycles Ω = {ωt}t∈[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the K-theory groups of the twisted groupoid C∗-algebras: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)). Building on our earlier work in [4, 5], we show that, if π : G → M is a locally trivial bundle of amenable groups over a locally compact Hausdorff space M, a homotopy Ω = {ωt}t∈[0,1] of 2-cocycles on G gives rise to an isomorphism: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)).

Original languageEnglish
Pages (from-to)1207-1229
Number of pages23
JournalRocky Mountain Journal of Mathematics
Volume46
Issue number4
DOIs
StatePublished - 2016

Keywords

  • 2-cocycle
  • Group bundle
  • K-theory
  • Twisted groupoid C∗-algebra

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