Anna Duwenig, Boyu Li
Published 2021-10-12, updated 2022-08-01Version 2
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 $\mathscr{B}$ and $\mathscr{C}$ and another equivalence between $\mathscr{C}$ and $\mathscr{D}$, we construct an equivalence between $\mathscr{B}$ and $\mathscr{D}$ out of the tensor product bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an equivalence relation.
The equivalence relations of local homeomorphisms and Fell algebras
The stable uniqueness theorem for equivariant Kasparov theory
II$_1$ factors and equivalence relations with distinct fundamental groups
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