{"paper":{"title":"Twists over \\'etale groupoids and twisted vector bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN","math.KT"],"primary_cat":"math.OA","authors_text":"Carla Farsi, Elizabeth Gillaspy","submitted_at":"2015-05-02T18:52:32Z","abstract_excerpt":"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 $\\mathcal{G}$.\n  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 $\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00364","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}