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arXiv · 2203.03476

Monotone cohomologies and oriented matchings

Luigi Caputi·Daniele Celoria·Carlo Collari
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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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Luigi Caputi, Daniele Celoria, Carlo Collari. 2022-03-07. Monotone cohomologies and oriented matchings. https://arxiv.org/abs/2203.03476

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