## Homology of path complexes and hypergraphs

Grigoryan A, Jimenez R, Muranov Y, Yau S-T (2019)
TOPOLOGY AND ITS APPLICATIONS 267: UNSP 106877.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Grigoryan, AlexanderUniBi; Jimenez, Rolando; Muranov, Yuri; Yau, Shing-Tung
Einrichtung
Abstract / Bemerkung
The path complex and its homology were defined in previous papers of the authors. The notion of a path complex is a natural discrete generalization of the notion of a simplicial complex. The theory of path complexes contains homotopy invariant homology theory of digraphs and (nondirected) graphs. In the paper we study the homology theory of path complexes. In particular, we describe functorial properties of paths complexes, introduce the notion of homotopy for path complexes and prove the homotopy invariance of path homology groups. We prove also several theorems that are similar to the results of classical homology theory of simplicial complexes. Then we apply this approach to construct homology theories on various categories of hypergraphs. We describe basic properties of these homology theories and relations between them. As a particular case, these results give new homology theories on the category of simplicial complexes. (C) 2019 Elsevier B.V. All rights reserved.
Stichworte
Path complex; Path homology of hypergraph; Graph homology; Homotopy of; path complexes; Simplicial complex
Erscheinungsjahr
2019
Zeitschriftentitel
TOPOLOGY AND ITS APPLICATIONS
Band
267
Art.-Nr.
UNSP 106877
ISSN
0166-8641
eISSN
1879-3207
Page URI
https://pub.uni-bielefeld.de/record/2939175

## Zitieren

Grigoryan A, Jimenez R, Muranov Y, Yau S-T. Homology of path complexes and hypergraphs. TOPOLOGY AND ITS APPLICATIONS. 2019;267: UNSP 106877.
Grigoryan, A., Jimenez, R., Muranov, Y., & Yau, S. - T. (2019). Homology of path complexes and hypergraphs. TOPOLOGY AND ITS APPLICATIONS, 267, UNSP 106877. doi:10.1016/j.topol.2019.106877
Grigoryan, Alexander, Jimenez, Rolando, Muranov, Yuri, and Yau, Shing-Tung. 2019. “Homology of path complexes and hypergraphs”. TOPOLOGY AND ITS APPLICATIONS 267: UNSP 106877.
Grigoryan, A., Jimenez, R., Muranov, Y., and Yau, S. - T. (2019). Homology of path complexes and hypergraphs. TOPOLOGY AND ITS APPLICATIONS 267:UNSP 106877.
Grigoryan, A., et al., 2019. Homology of path complexes and hypergraphs. TOPOLOGY AND ITS APPLICATIONS, 267: UNSP 106877.
A. Grigoryan, et al., “Homology of path complexes and hypergraphs”, TOPOLOGY AND ITS APPLICATIONS, vol. 267, 2019, : UNSP 106877.
Grigoryan, A., Jimenez, R., Muranov, Y., Yau, S.-T.: Homology of path complexes and hypergraphs. TOPOLOGY AND ITS APPLICATIONS. 267, : UNSP 106877 (2019).
Grigoryan, Alexander, Jimenez, Rolando, Muranov, Yuri, and Yau, Shing-Tung. “Homology of path complexes and hypergraphs”. TOPOLOGY AND ITS APPLICATIONS 267 (2019): UNSP 106877.
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