On a cohomology of digraphs and Hochschild cohomology

DOI10.1007/s40062-015-0103-1zbMath1353.05056OpenAlexW2171000028MaRDI QIDQ505027

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

Publication date: 18 January 2017

Published in: Journal of Homotopy and Related Structures (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40062-015-0103-1

zbMATH Keywords

Hochschild cohomologysimplicial complexcohomology theory of digraph

Mathematics Subject Classification ID

(Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) (13D03) Simplicial sets and complexes in algebraic topology (55U10) Directed graphs (digraphs), tournaments (05C20) Combinatorial aspects of simplicial complexes (05E45) Homotopy groups (55Q99)

Related Items

Path homology theory of edge-colored graphs ⋮ Magnitude homology and path homology ⋮ Singular cell homology ⋮ Homologies of transitive digraphs and discrete spaces;Гомологии транзитивных орграфов и дискретных пространств ⋮ Path complexes and their homologies ⋮ Path homology theory of multigraphs and quivers ⋮ Heat kernels on forms defined on a subgraph of a complete graph ⋮ Analysis and stochastic processes on metric measure spaces ⋮ The twisted homology of simplicial set ⋮ Biomolecular topology: modelling and analysis

Cites Work

• Simplicial cohomology is Hochschild cohomology
• Graphs associated with simplicial complexes
• Cohomology of digraphs and (undirected) graphs
• Contractible transformations do not change the homology groups of graphs
• Cohomology of incidence algebras and simplicial complexes
• Homotopy theory for digraphs
• Homology theory of graphs
• On the cohomology groups of an associative algebra
• On the Deformation of Algebra Morphisms and Diagrams
• Discrete differential calculus: Graphs, topologies, and gauge theory

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