2024/10/15 by Matthew C. B. Zaremsky, Zaremsky, Matthew C. B.
Chemistry · Computer Science · Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Graph theory and applications #Group Theory (math.GR) #Metric Geometry (math.MG) #Molecular spectroscopy and chirality #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2410.11993
openalex publication_date 2024/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a new, short proof of a result of Virk, that the Vietoris-Rips complex of the group ℤn with the standard word metric is contractible at large enough scales. This is inspired by a key observation in Virk's proof, but we use Bestvina-Brady discrete Morse theory to get a very short proof with better bounds. In the course of this, we get a new, general criterion for a metric space to have contractible Vietoris-Rips complexes at large enough scales, which could prove useful in the future.