Topology of Sobolev Maps
Topology of Sobolev Maps

Daniel Stern, Princeton University
Fine Hall 110
Given a homotopy class of maps between Riemannian manifolds, a classical question in geometric analysis asks whether one can find a representative minimizing some $L^p$ norm of the gradient. Attempts to answer this question lead one to consider Sobolev spaces of manifoldvalued maps, where one quickly encounters the problem that homotopy classes may not be welldefined. We will survey a series of results describing the homotopy structure of Sobolev maps, and discuss some related geometric variational problems.