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Characterizations of Forman curvature

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arxiv 2110.04554 v1 pith:BVO5EQ6X submitted 2021-10-09 math.DG

Jürgen Jost , Florentin Münch This is my paper · ORCID
classification math.DG
keywords formancurvatureboundscellscoincidecharacterizationscharacterizechoice
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We characterize Forman curvature lower bounds via contractivity of the Hodge Laplacian semigroup. We prove that Ollivier and Forman curvature coincide on edges when maximizing the Forman curvature over the choice of 2-cells. To this end, we translate between 2-cells and transport plans. Moreover, we give improved diameter bounds. We explicitly warn the reader that our Forman curvature notion does not coincide with Forman's original definition, but can be seen as generalization of the latter one.

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  1. Finding the Cores of Higher Graphs Using Geometric and Topological Means: A Survey

    math.HO 2025-06 accept novelty 2.0 of 10

    A structured review of geometric and topological methods for extracting small core representations from graphs, hypergraphs, and simplicial complexes.

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