Flat bundles with solvable holonomy

Goldman, William M.; Hirsch, Morris W.

doi:10.1090/S0002-9939-1981-0612747-0

Flat bundles with solvable holonomy
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by William M. Goldman and Morris W. Hirsch PDF

Proc. Amer. Math. Soc. 82 (1981), 491-494 Request permission

Abstract:

Let $G$ be a solvable linear Lie group. We show that for every flat principal $G$-bundle $\xi$ over a CW-complex $M$, there is a finite-sheeted covering space $p:\hat M \to M$ such that ${p^ * }\xi$ is trivial as a principal $G$-bundle. This result is used to show that every affine manifold with solvable fundamental group has a finite covering which is parallelizable.

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