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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Flat bundles with solvable holonomy


Authors: William M. Goldman and Morris W. Hirsch
Journal: Proc. Amer. Math. Soc. 82 (1981), 491-494
MSC: Primary 57R15; Secondary 55R15, 57R22
DOI: https://doi.org/10.1090/S0002-9939-1981-0612747-0
MathSciNet review: 612747
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0612747-0
Keywords: Solvable Lie group, flat bundle, covering space, affine manifold
Article copyright: © Copyright 1981 American Mathematical Society