Path Complexes and their Homologies

Path Complexes and their Homologies

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...

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Veröffentlicht in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-08, Vol.248 (5), p.564-599
Hauptverfasser: Grigor’yan, A. A., Lin, Yong, Muranov, Yu. V., Yau, Shing-Tung
Format: Artikel
Sprache:eng
Schlagworte:
Cartesian coordinates
Graph theory
Homology
Mathematics
Mathematics and Statistics
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Zusammenfassung: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-04897-9