Mathematics

A homotopy between two continuous  maps (between given manifolds) is a continuous deformation of one into the other. However, to minimize a Dirichlet energy in a given homotopy class one has to consider Sobolev maps, which no longer need to be continuous. The notion of homotopy between such maps therefore needs to be revisited. I will present a couple of definitions for homotopy between sobolev maps and talk about how they are connected to each other.