Twists over \'etale groupoids and twisted vector bundles

Carla Farsi; Elizabeth Gillaspy

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arXiv · 1505.00364

Twists over \'etale groupoids and twisted vector bundles

Carla Farsi·Elizabeth Gillaspy

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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 \'etale 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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BibTeX RIS

Carla Farsi, Elizabeth Gillaspy. 2015-05-02. Twists over \'etale groupoids and twisted vector bundles. https://arxiv.org/abs/1505.00364

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