Geometria Complessa e Geometria Differenziale
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L. Caputi - D. Celoria - C. Collari

Monotone cohomologies and oriented matchings

created by collari on 10 Aug 2022
modified on 15 Nov 2023


Accepted Paper

Inserted: 10 aug 2022
Last Updated: 15 nov 2023

Journal: Homology, Homotopy and Applications
Year: 2022

ArXiv: 2203.03476 PDF


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.

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