Distances between homotopy classes of $W^{s,p}({\mathbb{S}}^N;{\mathbb{S}}^N)$

Abstract

We introduce an equivalence relation on $W^{s,p}({\mathbb{S}}^N;{\mathbb{S}}^N)$ involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases we even obtain exact formulas.