The Gromov-Hausdorff Distance Between Spheres

Explore the Gromov-Hausdorff distance between spheres in this 50-minute lecture from the Applied Algebraic Topology Network. Discover general upper and lower bounds for d_GH(S^m,S^n) between spheres S^m and S^n with round metrics, where m < n and both are integers from 0 to infinity. Examine lower bounds derived from topological concepts related to the Borsuk-Ulam theorem. Learn about explicit constructions of optimal correspondences proving the tightness of lower bounds in specific cases, including d_GH(S^0,S^n), d_GH(S^m,S^infinity), d_GH(S^1,S^2), d_GH(S^1,S^3), and d_GH(S^2,S^3). Engage with open questions in this field of study, gaining insights into advanced topics in geometric topology and metric geometry.