• Corpus ID: 235490328

Systolic inequalities for the number of vertices

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