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

Teng Zhang

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arXiv · 2607.15096

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

Teng Zhang

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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 $C_u^*(X,\mathcal E)\cong C_u^*(Y,\mathcal F)$ 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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Teng Zhang. 2026-07-16. Isomorphism rigidity of uniform Roe algebras over arbitrary uniformly locally finite coarse spaces. https://arxiv.org/abs/2607.15096

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