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Path Complexes and their Homologies

Abstract

We introduce the notions of a path complex and its homologies. Particular cases of path homologies are simplicial homologies and digraph homologies. We state and prove some properties of path homologies, in particular, the K¨unneth formulas for Cartesian product and join, which happen to be true at the level of chain complexes.

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Correspondence to A. A. Grigor’yan or Yong Lin or Yu. V. Muranov or Shing-Tung Yau.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 5, pp. 79–128, 2016.

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Grigor’yan, A.A., Lin, Y., Muranov, Y.V. et al. Path Complexes and their Homologies. J Math Sci 248, 564–599 (2020). https://doi.org/10.1007/s10958-020-04897-9

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