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.
Clique complexes and graph powers.Israel Journal of Mathematics, 196(1):295– 319, 2013
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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.