On the path homology theory of digraphs and Eilenberg-Steenrod axioms

DOI10.4310/HHA.2018.v20.n2.a9zbMath1391.05125WikidataQ129758158 ScholiaQ129758158MaRDI QIDQ721490

Alexander Grigor'yan, Rolando Jiménez, Shing Tung Yau, Yurij V. Muranov

Publication date: 19 July 2018

Published in: Homology, Homotopy and Applications (Search for Journal in Brave)

zbMATH Keywords

Eilenberg-Steenrod axiomshomology of digraphshomotopy theory for digraphspaths in digraphs

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Relations of low-dimensional topology with graph theory (57M15) Axioms for homology theory and uniqueness theorems in algebraic topology (55N40) Directed graphs (digraphs), tournaments (05C20) Other homology theories in algebraic topology (55N35) Suspensions (55P40) Graph operations (line graphs, products, etc.) (05C76)

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Aspects of topological approaches for data science ⋮ Alexandroff homology and path homology ⋮ Path homology theory of edge-colored graphs ⋮ Cubical and simplicial sets in the category of quivers ⋮ Magnitude homology and path homology ⋮ Persistent path Laplacian ⋮ Homologies of transitive digraphs and discrete spaces;Гомологии транзитивных орграфов и дискретных пространств ⋮ Simplicial approach to path homology of quivers, marked categories, groups and algebras ⋮ Path homology theory of multigraphs and quivers ⋮ Homology of digraphs ⋮ Heat kernels on forms defined on a subgraph of a complete graph ⋮ Homology of path complexes and hypergraphs ⋮ Biomolecular topology: modelling and analysis ⋮ The embedded homology of hypergraph pairs

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