Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
Combinatorics
2023-08-17 v2 Algebraic Topology
General Topology
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.
Keywords
Cite
@article{arxiv.2110.11206,
title = {Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology},
author = {Luigi Caputi and Carlo Collari and Sabino Di Trani},
journal= {arXiv preprint arXiv:2110.11206},
year = {2023}
}
Comments
33 pages, 20 figures, 2 tables. Shortened, exposition improved, minor changes. To appear in Journal of Algebraic Combinatorics