# Systolic inequalities for the number of vertices

@inproceedings{Avvakumov2021SystolicIF, title={Systolic inequalities for the number of vertices}, author={Sergey Avvakumov and Alexey Balitskiy and Alfredo Hubard and Roman N. Karasev}, year={2021} }

. 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…

## One Citation

Systolic almost-rigidity modulo 2

- Mathematics
- 2022

. No power law systolic freedom is possible for the product of mod 2 systoles of dimension 1 and codimension 1. This means that any closed n dimensional Riemannian manifold M of bounded local…

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