Twists over \'etale groupoids and twisted vector bundles
Carla Farsi, Elizabeth Gillaspy

TL;DR
This paper investigates conditions under which twists over étale groupoids admit twisted vector bundles, linking these conditions to the Brauer group and classifying space properties, advancing understanding in twisted K-theory.
Contribution
It establishes criteria involving classifying spaces for torsion twists over étale groupoids to admit twisted vector bundles, connecting to the Brauer group.
Findings
Twists admitting twisted vector bundles form a subgroup of the Brauer group.
Conditions involving the classifying space $B ext{G}$ imply the existence of twisted vector bundles for torsion twists.
Provides new insights into the structure of twists in twisted K-theory.
Abstract
Inspired by recent papers on twisted -theory, we consider in this article the question of when a twist over a locally compact Hausdorff groupoid (with unit space a CW-complex) admits a twisted vector bundle, and we relate this question to the Brauer group of . We show that the twists which admit twisted vector bundles give rise to a subgroup of the Brauer group of . When is an \'etale groupoid, we establish conditions (involving the classifying space of ) which imply that a torsion twist over admits a twisted vector bundle.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
