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Proceedings of the American Mathematical Society

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The signature of fiber bundles

Author: James A. Schafer
Journal: Proc. Amer. Math. Soc. 33 (1972), 548-550
MSC: Primary 55F10; Secondary 57A65
MathSciNet review: 0324696
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Abstract: Let $ Y\hookrightarrow Z\underrightarrow \pi X$ be a locally trivial fiber bundle in the category of oriented topological manifolds. It is shown that if the identity component of the structure group G has finite index, then (signature of Z)=(signature of X) $ \blacksquare$ (signature of Y).

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Keywords: Fiber bundle, topological manifold, signature, cross sections, covering spaces
Article copyright: © Copyright 1972 American Mathematical Society

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