6 sep 2021 -- 16:10   [open in google calendar]

Abstract.

We introduce an operator S on vector-valued maps u which has the ability to capture the relevant topological information carried by u. In particular, this operator is defined on maps that take values in a closed submanifold N of the Euclidean space R^m, and coincides with the distributional Jacobian in case N is a sphere. More precisely, the range of S is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. We use S to characterise strong limits of smooth N -valued maps with respect to Sobolev norms, extending a result by Pakzad and Riviere. Moreover, we apply it to the study of the asymptotic behaviour of minimisers of Ginzburg-Landau type functionals arising in materials science. This is joint work with G. Canevari (Verona).