Vietoris-Rips complexes of n-by-n torus grids are shown to be tori, spheres, or wedges of spheres for several infinite families of grid sizes and scales.
On Vietoris–Rips complexes of hypercube graphs.Journal of Applied and Computational Topology, 6(2):177–192, 2022
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Vietoris-Rips complexes of torus grids
Vietoris-Rips complexes of n-by-n torus grids are shown to be tori, spheres, or wedges of spheres for several infinite families of grid sizes and scales.