Title: Interaction energy between vortices of vector fields on Riemannian surfaces,
Abstract: We study a variational Ginzburg-Landau type model depending on a small
parameter $\epsilon>0$ for (tangent) vector fields on a $2$-dimensional
Riemannian surface. As $\epsilon\to 0$, the vector fields tend to be of unit
length and will have singular points of a (non-zero) index, called vortices.
Our main result determines the interaction energy between these vortices as a
$\Gamma$-limit (at the second order) as $\epsilon\to 0$.