A definition of graph homology and graph K-theory of algebras

1999/11/15 by M. V. Movshev, Movshev, M. V.
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA) #math.KT #math.QA

paper · pdf · doi:10.48550/arxiv.math/9911111

26 pages, Latex

arxiv created 1999/11/15 · arxiv updated 2009/11/30

Abstract

We introduce and study elementary properties of graph homology of algebras. This new homology theory shares many features of cyclic and Hochschild homology. We also define a graph K-theory together with an analog of Chern character.

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• Homology for higher-rank graphs and twisted C*-algebras
• Graph homology computations
• Graph magnitude homology via algebraic Morse theory
• Mapping graph homology to K-theory of Roe algebras
• Applications of topological cyclic homology to algebraic K-theory