Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets and to provide computational tools for multipath cohomology. In particular, we develop acyclicity criteria and provide computations of multipath cohomology groups of oriented linear graphs. We further interpret the path poset as the face poset of a simplicial complex, and we investigate realisability problems.
Combinatorial and topological aspects of path posets, and multipath cohomology / Caputi, L.; Collari, C.; Di Trani, S.. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - 57:2(2023), pp. 617-658. [10.1007/s10801-022-01180-9]
Combinatorial and topological aspects of path posets, and multipath cohomology
Di Trani S.
2023
Abstract
Multipath cohomology is a cohomology theory for directed graphs, which is defined using the path poset. The aim of this paper is to investigate combinatorial properties of path posets and to provide computational tools for multipath cohomology. In particular, we develop acyclicity criteria and provide computations of multipath cohomology groups of oriented linear graphs. We further interpret the path poset as the face poset of a simplicial complex, and we investigate realisability problems.| File | Dimensione | Formato | |
|---|---|---|---|
|
Caputi_Combinatorial_2022.pdf
accesso aperto
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Creative commons
Dimensione
1.04 MB
Formato
Adobe PDF
|
1.04 MB | Adobe PDF |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
