Note on quasifibrations and manifolds

Stöcker, Ralph

doi:10.1090/S0002-9939-1974-0334204-8

Note on quasifibrations and manifolds
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by Ralph Stöcker PDF

Proc. Amer. Math. Soc. 43 (1974), 219-225 Request permission

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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