On coarse directed limits of metric spaces

DOI10.1216/RMJ.2023.53.1933zbMath1529.51005OpenAlexW4390105640MaRDI QIDQ6185027

Rui Tian, Chi-Keung Ng

Publication date: 5 January 2024

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/rocky-mountain-journal-of-mathematics/volume-53/issue-6/ON-COARSE-DIRECTED-LIMITS-OF-METRIC-SPACES/10.1216/rmj.2023.53.1933.full

zbMATH Keywords

metric spacesasymptotic dimensionbounded geometryproperty Auniformly locally finitecoarse spacesdirected limitscoarse property Cfinite weak coarse decomposition complexity

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Dimension theory in general topology (54F45) General theory of distance geometry (51K05) Dimension theory in algebraic topology (55M10) Lipschitz and coarse geometry of metric spaces (51F30)

Cites Work

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• Coarse metric approximation
• Asymptotic dimension of coarse spaces.
• An alternative definition of coarse structures
• The Novikov conjecture for groups with finite asymptotic dimension
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• \(C^*\)-algebras and controlled topology
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• Property A for coarse spaces
• General uniform Roe algebra rigidity
• Asymptotic filtered colimits
• Coarse property C and decomposition complexity
• Coarse metric and uniform metric
• Asymptotic topology

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