Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces

2026/07/16 by Teng Zhang · 1 citation
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Abstract

Let (X,\mathcal E) and (Y,\mathcal F) be uniformly locally finite coarse spaces. We prove that every C^*-algebra isomorphism C_u^*(X,\mathcal E)≅ C_u^*(Y,\mathcal F) forces (X,\mathcal E) and (Y,\mathcal F) to be bijectively coarsely equivalent. This completely resolves the isomorphism rigidity problem for uniform Roe algebras over arbitrary uniformly locally finite coarse spaces.

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