Year: 2021
Type: article
Abstract: Many simplicial complexes arising in practice have an associated metric space structure on the vertex set but not on the complex, e.g. the Vietoris-Rips complex in applied topology. We formalize a remedy by introducing a category of simplicial metric thickenings whose objects have a natural realization as metric spaces. The properties of this category allow us to prove that, for a large class of thickenings including Vietoris-Rips and Cech thickenings, the product of metric thickenings is homotopy equivalent to the metric thickenings of product spaces, and similarly for wedge sums.
DOI: 10.4204/eptcs.333.18
Authors: Henry Adams, Johnathan Bush, Joshua Mirth
Institution: Colorado State University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
Funder: Colorado State University
OpenAlex ID: W3123395315