Homology, Homotopy and Applications

Volume 24 (2022)

Number 2

Path homology of directed hypergraphs

Pages: 347 – 363

DOI: https://dx.doi.org/10.4310/HHA.2022.v24.n2.a18

Authors

Yuri Muranov (Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland)

Anna Szczepkowska (Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland)

Vladimir Vershinin (Département des Sciences Mathématiques, Université de Montpellier, France)

Abstract

We describe various path homology theories constructed for a directed hypergraph. We introduce the category of directed hypergraphs and the notion of a homotopy in this category. Also, we investigate the functoriality and the homotopy invariance of the introduced path homology groups.We provide examples of computation of these homology groups.

Keywords

path complex, directed hypergraph, path homology, digraph, homotopy of a directed hypergraph

2010 Mathematics Subject Classification

05C20, 05C22, 05C25, 05C65, 55N35, 55U05

Received 5 October 2021

Received revised 4 December 2021

Accepted 6 December 2021

Published 14 September 2022