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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 over metric spaces that are coarse unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent.more » « less
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We study which von Neumann algebras can be embedded into uniform Roe algebras and quasi-local algebras associated with a uniformly locally finite metric space X. Under weak assumptions, these C*-algebras contain embedded copies of certain matrix algebras. We aim to show they cannot contain any other von Neumann algebras. One of our main results shows that the only embedded von Neumann algebras are the “obvious” ones.more » « less
