Contractible Vietoris–Rips complexes of ℤⁿ

We give a new, short proof of a result of Virk, that the Vietoris–Rips complex of the group Z n 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.