We are concerned with properties of H-1/2(Omega; S-1) where Omega is the bo
undary 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-infin
ity(Omega; S-1) in H-1/2 coincides With the u's such that T(u) = 0. Moreove
r, 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 proble
m. (C) 2000 Academie des sciences/Editions scientifiques ct medicales Elsev
ier SAS.