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C*-rigidity of bounded geometry metric spaces

· 2025 · math.OA · arXiv 2501.03128

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abstract

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 a metric space of bounded geometry is canonically isomorphic to the group of coarse equivalences of the space up to closeness.

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Rigidity of Higson coronas

math.LO · 2025-02-14 · conditional · novelty 8.0

Under OCA and MA_ℵ1, homeomorphic Higson coronas of uniformly locally finite metric spaces force coarse equivalence, a statement independent of ZFC.

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  • Rigidity of Higson coronas math.LO · 2025-02-14 · conditional · none · ref 23 · internal anchor

    Under OCA and MA_ℵ1, homeomorphic Higson coronas of uniformly locally finite metric spaces force coarse equivalence, a statement independent of ZFC.