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Coarse equivalence versus bijective coarse equivalence of expander graphs

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arxiv 2307.11529 v1 pith:RQSRMZVD submitted 2023-07-21 math.MG math.FAmath.OA

Florent Baudier , Bruno de Mendonça Braga , Ilijas Farah , Alessandro Vignati , Rufus Willett This is my paper · ORCID
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keywords coarseequivalencegraphsbijectivedisjointexpanderunionsalgebras
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We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras of coarse disjoint unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent.

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  1. C*-rigidity of bounded geometry metric spaces

    math.OA 2025-01 accept novelty 8.0 of 10

    Uniformly locally finite metric spaces with isomorphic Roe algebras are coarsely equivalent, and the outer automorphism group of the Roe algebra is canonically isomorphic to the group of coarse equivalences.

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