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On $ 4$-manifolds with finitely dominated covering spaces


Author: Jonathan A. Hillman
Journal: Proc. Amer. Math. Soc. 121 (1994), 619-626
MSC: Primary 57N13
DOI: https://doi.org/10.1090/S0002-9939-1994-1204375-2
MathSciNet review: 1204375
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1994-1204375-2
Keywords: Finitely dominated, 4-manifold, mapping torus, $ P{D_3}$-complex, surface bundle
Article copyright: © Copyright 1994 American Mathematical Society

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