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

Tomas L. Gomez; Francisco Presas

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

Tomas L. Gomez·Francisco Presas

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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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Tomas L. Gomez, Francisco Presas. 1999-12-06. Affine representations of the fundamental group (with an appendix on parabolic representations). https://arxiv.org/abs/math/9912043

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