On the structure of the Sobolev space H1/2 with values into the circle

We are concerned with properties of H-1/2(Omega; S-1) where Omega is the boundary of a domain in R-3. To every u is an element of H-1/2(Omega; S-1) we associate a distribution T(u) which, in some sense, describes the location and the topological degree of singularities of u. The closure Y of C-infinity(Omega; S-1) in H-1/2 coincides With the u's such that T(u) = 0. Moreover, every u is an element of Y admits a unique (mod. 2 pi) lifting in H-1/2 + W-1,W-1. We also discuss an application to the 3-d Ginzburg-Landau problem. (C) 2000 Academie des sciences/Editions scientifiques ct medicales Elsevier SAS.