Fedor Manin - Linear Nullhomotopies of Maps to Spheres

Explore the intricacies of building nullhomotopies of maps to simply connected spaces with controlled Lipschitz constant in this 46-minute conference talk by Fedor Manin. Delve into the complexities of maps between spheres, focusing on the theorem that every nullhomotopic, L-Lipschitz map from S^m to S^n has a C(m,n) · (L+1)-Lipschitz nullhomotopy. Learn about key concepts such as the geodesic loop, metrics, simplicial maps, and specific cases like maps from S2 to S2. Gain insights from joint and separate work with Chambers, Dotterrer, Weinberger, Berdnikov, and Guth as you progress through topics including the warmup theorem, homotopy, and their practical applications in algebraic topology.