Title:
Vertex numbers of simplicial complexes with free abelian fundamental group
Author(s):
Frick, Florian; Superdock, Matt
Year of publication:
2025
Available Date:
2025-04-09T13:03:08Z
Abstract:
We show that the minimum number of vertices of a simplicial complex with fundamental group ℤn is at most O(n) and at least Ω(n3/4). For the upper bound, we use a result on orthogonal 1-factorizations of K2n. For the lower bound, we use a fractional Sylvester–Gallai result. This application of extremal results in discrete geometry seems to be new. We also prove that any group presentation ⟨S|R⟩ ≅ ℤn whose relations are of the form gahbic for g, h, i ∈ S has at least Ω(n3/2) generators.
Part of Identifier:
e-ISSN (online): 1855-3974
Keywords:
Simplicial complex
fundamental group
incidence geometry
DDC-Classification:
510 Mathematik
Publication Type:
Wissenschaftlicher Artikel
URL of the Original Publication:
DOI of the Original Publication:
Journaltitle:
Ars Mathematica Contemporanea
Department/institution:
Mathematik und Informatik
Institut für Mathematik