Cohomology of digraphs and (undirected) graphs

DOI10.4310/AJM.2015.v19.n5.a5zbMath1329.05132OpenAlexW2563142987MaRDI QIDQ906641

Yong Lin, Alexander Grigor'yan, Yurij V. Muranov, Shing Tung Yau

Publication date: 22 January 2016

Published in: The Asian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/ajm.2015.v19.n5.a5

zbMATH Keywords

differential graded algebrassimplicial homologycohomology of digraphspath complex of a digraphcohomology of graphsdifferential calculi on algebras

Mathematics Subject Classification ID

Paths and cycles (05C38) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Relations of low-dimensional topology with graph theory (57M15) Differential graded algebras and applications (associative algebraic aspects) (16E45) Simplicial sets and complexes in algebraic topology (55U10) Directed graphs (digraphs), tournaments (05C20) Chain complexes (category-theoretic aspects), dg categories (18G35) Other homology theories in algebraic topology (55N35)

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Aspects of topological approaches for data science ⋮ Alexandroff homology and path homology ⋮ Path homology theory of edge-colored graphs ⋮ On homology theories of cubical digraphs ⋮ Discrete differential calculus on simplicial complexes and constrained homology ⋮ Discrete cubical and path homologies of graphs ⋮ Singular cell homology ⋮ Persistent path Laplacian ⋮ Homologies of transitive digraphs and discrete spaces;Гомологии транзитивных орграфов и дискретных пространств ⋮ Path complexes and their homologies ⋮ On a cohomology of digraphs and Hochschild cohomology ⋮ Path homology theory of multigraphs and quivers ⋮ Homology of digraphs ⋮ Heat kernels on forms defined on a subgraph of a complete graph ⋮ Analysis and stochastic processes on metric measure spaces ⋮ Homology of path complexes and hypergraphs ⋮ Existence and uniqueness of solutions to the norm minimum problem on digraphs ⋮ The twisted homology of simplicial set ⋮ Biomolecular topology: modelling and analysis ⋮ An efficient algorithm for 1-dimensional (Persistent) path homology

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