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 07 Oct 2024

[BibTeX]

Published Paper

Inserted: 10 aug 2022
Last Updated: 7 oct 2024

Journal: Homology, Homotopy and Applications
Volume: 26
Number: 2
Pages: 137 – 161
Year: 2022
Doi: 10.4310/HHA.2024.v26.n2.a7

ArXiv: 2203.03476 PDF

Abstract:

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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