Affine representations of the fundamental group (with an appendix on parabolic representations)
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Publication:6501573
arXivmath/9912043MaRDI QIDQ6501573
Francisco Presas, Tomás L. Gómez
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.
Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Homotopy theory and fundamental groups in algebraic geometry (14F35) Holomorphic bundles and generalizations (32L05)
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