#### Abstract

Certain Sobolev spaces of *S*^{1}-valued functions can be
written as a disjoint union of homotopy classes. The problem of
finding the distance between different homotopy classes in such
spaces is considered. In particular several types of
one-dimensional and two-dimensional domains are studied. Lower
bounds are derived for these distances. Furthermore, in many cases
it is shown that the lower bounds are sharp but are not achieved.

This is a joint work with Jacob Rubinstein

*TUESDAY, December 6, 2005*

**Time:** 1:30 P.M.

**Location:** PPB 300