Work

Vertex numbers of simplicial complexes with free abelian fundamental group

Year: 2025

Type: article

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.

Source: Refubium (Universitätsbibliothek der Freien Universität Berlin)

DOI: 10.17169/refubium-46979

Authors: Frick, Florian, Superdock, Matt

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: CAREER: Geometric and Topological Combinatorics, G6671297155, Topological Methods for Discrete Problems

OpenAlex ID: W6887610869