Equivalence of Fell bundles is an equivalence relation

2021/10/12 by Anna Duwenig, Boyu Li, Duwenig, Anna +1
Mathematics · Medicine · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Ophthalmology and Eye Disorders

paper · pdf · doi:10.48550/arxiv.2110.06343

Abstract

We introduce the notion of groupoid pre-equivalences and prove that they give rise to groupoid equivalences by taking certain quotients. Then, given an equivalence of Fell bundles \mathscrB and \mathscrC and another equivalence between \mathscrC and \mathscrD, we construct an equivalence between \mathscrB and \mathscrD out of the tensor product bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an equivalence relation.

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