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

1999/12/06 by Tomas L. Gomez, Francisco Presas, Gomez, Tomas L. +1
Mathematics · #14F05 #14F35 #32L05 #53C07 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F05 #msc:14F35 #msc:32L05 #msc:53C07

paper · pdf · doi:10.48550/arxiv.math/9912043

13 pages, LaTeX2e

arxiv created 1999/12/06 · arxiv updated 2009/11/30

Abstract

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.

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