2014/02/13 by Elizabeth Gillaspy, Gillaspy, Elizabeth
Mathematics · #46L55 #46L80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA) #math.KT #math.OA #msc:46L55 #msc:46L80
paper · pdf · doi:10.48550/arxiv.1402.3280
Some improvements to the exposition; also, the hypotheses on Theorem 5.1 have been relaxed so that X is no longer required to be compact. This version (v3) fixes the erroneous argument in v2 for this strengthening of Theorem 5.1. This is the version that will appear in the Journal of Operator Theory
openalex publication_date 2014/02/13 · arxiv created 2014/09/08 · arxiv updated 2014/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper constitutes a first step in the author's program to investigate 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 reduced twisted groupoid C^*-algebras: K_*(C^*r(G, ω0)) ≅ K_*(C^*r(G, ω1)). Generalizing work of Echterhoff, Lück, Phillips, and Walters from 2010, we show that if G = G \ltimes X is a second countable locally compact transformation group, then whenever G satisfies the Baum-Connes conjecture with coefficients, a homotopy ω= \ωt\t ∈ [0,1] of 2-cocycles on G \ltimes X gives rise to an isomorphism K_*(C^*r(G \ltimes X, ω0)) ≅ K_*(C^*r(G \ltimes X, ω1)).