Published on *Department of Mathematics* (https://math.yale.edu)

August 1, 2019 - 4:00pm

LOM 206

In a 1978 paper, Gromov explained how the Lipschitz constant of a map S^n -> Y, where Y is a simply connected compact Riemannian manifold, restricts its homotopy class. He later conjectured that the bounds obtained there are asymptotically sharp. For example, this would imply that if Y is a closed oriented n-manifold with a disk cut out, then one could always find a C(Y)L-Lipschitz map which is homotopic to L^n times the puncture, even though you can only get

L^{n-1} by winding around the puncture. I will show that this is not always the case. If there is time I will also discuss how the same techniques apply to the problem of finding efficient homotopies between Lipschitz maps.