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<p>We prove that uniformly locally finite metric spaces with isomorphic Roe algebras must be coarsely equivalent. As an application, we also prove that the outer automorphism group of the Roe algebra of such a metric space is canonically isomorphic to the group of coarse equivalences of the space up to closeness.</p>

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C*-rigidity of bounded geometry metric spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年3月4日

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  • Diego Martínez,
  • Federico Vigolo

摘要

We prove that uniformly locally finite metric spaces with isomorphic Roe algebras must be coarsely equivalent. As an application, we also prove that the outer automorphism group of the Roe algebra of such a metric space is canonically isomorphic to the group of coarse equivalences of the space up to closeness.