2018/10/17 by Bruno de Mendonça Braga, Braga, Bruno de Mendonça, Ilijas Farah +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Logic (math.LO) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1810.07789
openalex publication_date 2018/10/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
A uniform Roe corona is the quotient of the uniform Roe algebra of a metric space by the ideal of compact operators. Among other results, we show that it is consistent with ZFC that isomorphism between uniform Roe coronas implies coarse equivalence between the underlying spaces, for the class of uniformly locally finite metric spaces which coarsely embed into a Hilbert space. Moreover, for uniformly locally finite metric spaces with property A, it is consistent with ZFC that isomorphism between the uniform Roe coronas is equivalent to bijective coarse equivalence between some of their cofinite subsets. We also find locally finite metric spaces such that the isomorphism of their uniform Roe coronas is independent of ZFC. All set-theoretic considerations in this paper are relegated to two 'black box' principles.