A. A. Grigor'yan, Yong Lin, Yu. V. Muranov, Shing-Tung Yau, “Path complexes and their homologies”, Fundam. Prikl. Mat., 2016, Volume 21, Issue 5,Pages <nobr>79

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Path complexes and their homologies

A. A. Grigor'yan^ab, Yong Lin^c, Yu. V. Muranov^d, Shing-Tung Yau^e

^a Department of Mathematics, University of Bielefeld, 33613 Bielefeld, Germany
^b Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
^c Department of Mathematics, Renmin University of China, Beijing 100872, P.R. China
^d Faculty of Mathematics and Computer Sciences, University of Warmia and Mazury, Olsztyn, Poland
^e Department of Mathematics, Harvard University, Cambridge MA 02138, USA

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 Künneth formulas for Cartesian product and join, which happen to be true at the level of chain complexes.

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