Monotone cohomologies and oriented matchings

Autor:	Caputi, Luigi, Celoria, Daniele, Collari, Carlo
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Topology 05C70 18G85
Druh dokumentu:	Working Paper
Popis:	In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs, and focus on their (twisted) cohomology groups. We characterise oriented matchings in terms of induced free-flow pseudoforests, and explicitly determine the homotopy type of the associated simplicial complexes. Furthermore, we provide a connection between the cohomology of oriented matchings with certain functor coefficients, and the recently defined multipath cohomology. Finally, we define a further oriented homology for graphs and interpret it as a count of free-flow orientations. Comment: 18 pages, 10 figures, comments are welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2203.03476 Zobrazit plný text záznamu View this record from Arxiv