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Oriented manifolds that fiber over $ S\sp{4}$


Author: Steven M. Kahn
Journal: Trans. Amer. Math. Soc. 286 (1984), 839-850
MSC: Primary 57R75
DOI: https://doi.org/10.1090/S0002-9947-1984-0760991-1
MathSciNet review: 760991
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Abstract: Necessary and sufficient conditions are given for an oriented manifold $ M$ to fiber up to cobordism over the $ 4$-sphere $ {S^4}$ (i.e. for $ M$ to be oriented cobordant to a fiber bundle over $ {S^4}$). The result here extends those previously obtained for fiberings over $ {S^1}$ and $ {S^2}$.

In addition, fiberings over products of surfaces are studied with complete solutions (in the sense above) being given in most cases including those of $ {S^2} \times {S^2}$ and $ {({S^1})^4}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0760991-1
Keywords: Oriented cobordism class, fibration, Stiefel-Whitney numbers, Wu class, Wall's ring
Article copyright: © Copyright 1984 American Mathematical Society

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