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Proceedings of the American Mathematical Society

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

 

 

Note on quasifibrations and manifolds


Author: Ralph Stöcker
Journal: Proc. Amer. Math. Soc. 43 (1974), 219-225
MSC: Primary 55F15
DOI: https://doi.org/10.1090/S0002-9939-1974-0334204-8
MathSciNet review: 0334204
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Abstract: Let $ E$ be a closed $ {C^\infty }$-manifold which is the total space of a quasifibration over $ {S^n}$ with fibre $ {S^k}$. Then, in many cases, $ E$ has the homotopy type of an orthogonal $ {S^k}$-bundle over $ {S^n}$. The proof includes a classification theorem for certain quasifibrations which has further applications.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0334204-8
Keywords: Quasifibration, manifold, orthogonal bundle, fibre homotopy type
Article copyright: © Copyright 1974 American Mathematical Society