2015/05/02 by Farsi, Carla, Gillaspy, Elizabeth
#19L50 #46L55 #46L80 #46M20 (Secondary) #54H15 #55R25 (Primary) #FOS: Mathematics #General Topology (math.GN) #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1505.00364
Inspired by recent papers on twisted K-theory, we consider in this article the question of when a twist R over a locally compact Hausdorff groupoid G (with unit space a CW-complex) admits a twisted vector bundle, and we relate this question to the Brauer group of G. We show that the twists which admit twisted vector bundles give rise to a subgroup of the Brauer group of G. When G is an étale groupoid, we establish conditions (involving the classifying space BG of G) which imply that a torsion twist R over G admits a twisted vector bundle.