Oriented manifolds that fiber over 𝑆⁴

Kahn, Steven M.

doi:10.1090/S0002-9947-1984-0760991-1

Oriented manifolds that fiber over $S^{4}$
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Trans. Amer. Math. Soc. 286 (1984), 839-850 Request permission

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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