2013/08/06 by Indira Chatterji, Chatterji, Indira, Guido Mislin +3
Mathematics · #22D05 #55R10 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1308.1412
openalex publication_date 2013/08/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.