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Proceedings of the American Mathematical Society

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

 

 

The signature of fiber bundles


Author: James A. Schafer
Journal: Proc. Amer. Math. Soc. 33 (1972), 548-550
MSC: Primary 55F10; Secondary 57A65
DOI: https://doi.org/10.1090/S0002-9939-1972-0324696-0
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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DOI: https://doi.org/10.1090/S0002-9939-1972-0324696-0
Keywords: Fiber bundle, topological manifold, signature, cross sections, covering spaces
Article copyright: © Copyright 1972 American Mathematical Society