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On homology theories
of cubical digraphs
Alexander Grigor’yan and Yuri Muranov |
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Vol. 322 (2023), No. 1, 39–58
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Abstract |
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We prove the equivalence of the singular cubical homology and the path homology on the category of cubical digraphs. As a corollary we obtain a new relation between the singular cubical homology of digraphs and simplicial homology. |
Keywords
homology of digraphs, equivalence of homology theories,
path homology theory, singular cubical homology theory,
cubical digraph, paths in digraphs
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Mathematical Subject Classification
Primary: 18G85, 55N10, 55N35, 57M15
Secondary: 05C20, 05C25, 05C38
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Milestones
Received: 22 January 2021
Revised: 23 November 2022
Accepted: 15 January 2023
Published: 3 May 2023
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Authors |
| Alexander Grigor’yan | |
| Department of Mathematics University of Bielefeld Bielefeld Germany |
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| Yuri Muranov | |
| Faculty of Mathematics and Computer
Science University of Warmia and Mazury in Olsztyn Olsztyn Poland |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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