Affine representations of the fundamental group (with an appendix on parabolic representations)

Tomas L. Gomez, Francisco Presas

Published 1999-12-06Version 1

Unitary representations of the fundamental group of a Kahler manifold correspond to polystable vector bundles (with vanishing Chern classes). Semisimple linear representations correspond to polystable Higgs bundles. In this paper we find the objects corresponding to affine representations: the linear part gives a Higgs bundle and the translation part corresponds to an element of a generalized de Rham cohomology.