A combinatorial approach to coarse geometry

DOI10.1016/j.topol.2011.10.012zbMath1273.54030arXiv0906.1372OpenAlexW1998880888MaRDI QIDQ409495

Matija Cencelj, Žiga Virk, Jerzy Dydak, Aleš Vavpetič

Publication date: 13 April 2012

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.1372

zbMATH Keywords

coarse geometryasymptotic dimensionsimplicial trees

Mathematics Subject Classification ID

Dimension theory in general topology (54F45) Dimension theory in algebraic topology (55M10) Shape theory in general topology (54C56) Shape theory (55P55)

Related Items (8)

Footprints of geodesics in persistent homology ⋮ Rips complexes as nerves and a functorial Dowker-nerve diagram ⋮ Reconstruction properties of selective Rips complexes ⋮ The persistent topology of optimal transport based metric thickenings ⋮ Approximations of 1-dimensional intrinsic persistence of geodesic spaces and their stability ⋮ Zig-zag chains and metric equivalences between ultrametric spaces ⋮ 1-Dimensional intrinsic persistence of geodesic spaces ⋮ Coarse metric approximation

Cites Work

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• An alternative definition of coarse structures
• Shape theory. An introduction
• Harmonic analysis, cohomology, and the large-scale geometry of amenable groups
• The coarse Baum-Connes conjecture for spaces which admit a uniform embedding into Hilbert space
• A note on spaces of asymptotic dimension one
• Filling invariants of systolic complexes and groups.
• On asymptotic dimension of countable Abelian groups.
• Asymptotic dimension of finitely presented groups
• Amenable group actions and the Novikov conjecture

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