Systolic inequalities for the number of vertices - Archive ouverte HAL
Article Dans Une Revue Journal of Topology and Analysis Année : 2023

Systolic inequalities for the number of vertices

Résumé

Inspired by the classical Riemannian systolic inequality of Gromov, we present a combinatorial analogue providing a lower bound on the number of vertices of a simplicial complex in terms of its edge-path systole. Similarly to the Riemannian case, where the inequality holds under a topological assumption of “essentiality”, our proofs rely on a combinatorial analogue of that assumption. Under a stronger assumption, expressed in terms of cohomology cup-length, we improve our results quantitatively. We also illustrate our methods in the continuous setting, generalizing and improving quantitatively the Minkowski principle of Balacheff and Karam; a corollary of this result is the extension of the Guth–Nakamura cup-length systolic bound from manifolds to complexes.

Dates et versions

hal-04500324 , version 1 (11-03-2024)

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Citer

Sergey Avvakumov, Alexey Balitskiy, Alfredo Hubard, Roman Karasev. Systolic inequalities for the number of vertices. Journal of Topology and Analysis, 2023, pp.1-23. ⟨10.1142/S179352532350005X⟩. ⟨hal-04500324⟩
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