Flat bundles with complex analytic holonomy. Auteur(s): Pittet C. (Document sans référence bibliographique) Ref HAL: hal-01145336_v1 Ref Arxiv: 1308.1412 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: Let G be a connected complex Lie group. We show that any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space if and only if each real characteristic class of positive degree of G vanishes. A third equivalent condition is that the derived group of the radical of G is simply connected. As a corollary, the same conditions are equivalent if G is a connected amenable Lie group. In particular, if G is a connected compact Lie group then any flat principal G-bundle over any finite CW-complex pulls back to a trivial bundle over some finite covering space of the base space.