Homotopy types of Vietoris–Rips complexes of hypercube graphs
Ziqin Feng · Journal of Topology and Analysis · 2025
We describe the homotopy types of Vietoris–Rips complexes of hypercube graphs at scale [Formula: see text]. We represent the vertices in the hypercube graph [Formula: see text] as the collection of all subsets of [Formula: see text] and equip [Formula: see text] with the metric using symmetric difference distance. It is proved in [M. Adamaszek and H. Adams, On Vietoris–Rips complexes of hypercube graphs, J. Appl. Comput. Topol. 6 (2022) 177–192] that the Vietoris–Rips complexes of hypercube graphs [Formula: see text] at scale [Formula: see text], [Formula: see text], are homotopy equivalent to [Formula: see text]-many spheres with dimension [Formula: see text] where [Formula: see text]. Questions are raised in the above-mentioned reference for determining the homotopy types of [Formula: see text] with large scales [Formula: see text]. We prove that for [Formula: see text], [Formula: see text]