The Gromov–Hausdorff distance between spheres
Sunhyuk Lim, Facundo Mémoli, Zane Smith · Geometry & Topology · 2023
We provide general upper and lower bounds for the Gromov-Hausdorff distance d GH .S m ; S n / between spheres S m and S n (endowed with the round metric) for 0 Ä m < n Ä 1.Some of these lower bounds are based on certain topological ideas related to the Borsuk-Ulam theorem.Via explicit constructions of (optimal) correspondences, we prove that our lower bounds are tight in the cases of d GH .S 0 ; S n /, d GH .S m ; S 1 /, d GH .