Flat bundles with complex analytic holonomy

Indira Chatterji; Guido Mislin; Christophe Pittet

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arXiv · 1308.1412

Flat bundles with complex analytic holonomy

Indira Chatterji·Guido Mislin·Christophe Pittet

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Abstract

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.

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BibTeX RIS

Indira Chatterji, Guido Mislin, Christophe Pittet. 2013-08-06. Flat bundles with complex analytic holonomy. https://arxiv.org/abs/1308.1412

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