  We study a natural map from representations of a free (resp. free abelian)
group of rank g in GL_r(C), to holomorphic vector bundles of degree zero over a
compact Riemann surface X of genus g (resp. complex torus X of dimension g).
This map defines what is called a Schottky functor. Our main result is that
this functor induces an equivalence between the category of unipotent
representations of Schottky groups and the category of unipotent vector bundles
on X. We also show that, over a complex torus, any vector or principal bundle
with a flat holomorphic connection is Schottky.

Algebraic Geometry;Differential Geometry