On 4-manifolds with finitely dominated covering spaces

Hillman, Jonathan A.

doi:10.1090/S0002-9939-1994-1204375-2

On $4$-manifolds with finitely dominated covering spaces
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Proc. Amer. Math. Soc. 121 (1994), 619-626 Request permission

Abstract:

We show that if the universal covering space $\widetilde {M}$ of a closed 4-manifold $M$ is finitely dominated then either $M$ is aspherical, or $\tilde M$ is homotopy equivalent to ${S^2}$ or ${S^3}$, or ${\pi _1}(M)$ is finite. We also give a criterion for a closed 4-manifold to be homotopy equivalent to one which fibres over the circle.

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