Discrete homology theory for metric spaces

DOI10.1112/blms/bdu043zbMath1308.55004arXiv1306.3915OpenAlexW3101241802MaRDI QIDQ2922856

Hélène Barcelo, Valerio Capraro, Jacob A. White

Publication date: 15 October 2014

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.3915

zbMATH Keywords

metric spacesgraphshomology theorycoarse homology\(A\)-theory

Mathematics Subject Classification ID

Algebraic combinatorics (05E99) Metric geometry (51F99) Other homology theories in algebraic topology (55N35)

Related Items (11)

Higher discrete homotopy groups of graphs ⋮ Discrete cubical and path homologies of graphs ⋮ On the Čech cohomology of Morse boundaries ⋮ The persistent topology of optimal transport based metric thickenings ⋮ Rigidity of warped cones and coarse geometry of expanders ⋮ Discrete fundamental groups of warped cones and expanders ⋮ Čech closure spaces: a unified framework for discrete and continuous homotopy ⋮ Path homology theory of multigraphs and quivers ⋮ Coarse fundamental groups and box spaces ⋮ Homology groups of cubical sets with connections ⋮ On the Vanishing of Discrete Singular Cubical Homology for Graphs

Cites Work

• Amenability, locally finite spaces, and bi-Lipschitz embeddings
• Gromov's theorem on groups of polynomial growth and elementary logic
• Coarse Baum-Connes conjecture
• Homotopy theory of graphs
• Perspectives on \(A\)-homotopy theory and its applications
• $k$-Parabolic subspace arrangements
• Controlled coarse homology and isoperimetric inequalities
• Aperiodic Tilings, Positive Scalar Curvature, and Amenability of Spaces
• A notion of continuity in discrete spaces and applications
• Coarse cohomology and index theory on complete Riemannian manifolds
• Axiomatic Approach to Homology Theory
• Foundations of a connectivity theory for simplicial complexes

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