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Twists over étale groupoids and twisted vector bundles


Authors: Carla Farsi and Elizabeth Gillaspy
Journal: Proc. Amer. Math. Soc. 144 (2016), 3767-3779
MSC (2010): Primary 46L55, 54H15, 55R25; Secondary 46L80, 46M20
DOI: https://doi.org/10.1090/proc/13165
Published electronically: May 6, 2016
MathSciNet review: 3513537
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Abstract: Inspired by recent papers on twisted $ K$-theory, we consider in this article the question of when a twist $ \mathcal {R}$ over a locally compact Hausdorff groupoid $ \mathcal {G}$ (with unit space a CW-complex) admits a twisted vector bundle, and we relate this question to the Brauer group of $ \mathcal {G}$. We show that the twists which admit twisted vector bundles give rise to a subgroup of the Brauer group of $ \mathcal {G}$. When $ \mathcal {G}$ is an étale groupoid, we establish conditions (involving the classifying space $ B\mathcal {G}$ of $ \mathcal {G}$) which imply that a torsion twist $ \mathcal {R}$ over $ \mathcal {G}$ admits a twisted vector bundle.


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Additional Information

Carla Farsi
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80301-0395

Elizabeth Gillaspy
Affiliation: Department of Mathematics, University of Colorado, Boulder, Colorado 80301-0395

DOI: https://doi.org/10.1090/proc/13165
Received by editor(s): May 2, 2015
Received by editor(s) in revised form: September 30, 2015
Published electronically: May 6, 2016
Communicated by: Varghese Mathai
Article copyright: © Copyright 2016 American Mathematical Society

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