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Proceedings of the American Mathematical Society

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Higher Whitehead groups of certain bundles over Seifert manifolds


Authors: A. J. Nicas and C. W. Stark
Journal: Proc. Amer. Math. Soc. 91 (1984), 1-5
MSC: Primary 18F25; Secondary 57T20
DOI: https://doi.org/10.1090/S0002-9939-1984-0735551-4
MathSciNet review: 735551
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Abstract: Vanishing results for $ {\text{W}}{{\text{h}}_j}({\pi _1}M) \otimes R(R = {\mathbf{Z}},{\mathbf{Q}},{\text{ or }}{\mathbf{Z}}[1/2])$ are obtained when $ M$ is a closed aspherical manifold which is the total space of a bundle over an insufficiently large Seifert manifold with infinite fundamental group of hyperbolic type. Allowable fibers include Riemannian flat manifolds and closed aspherical manifolds with poly- $ {\mathbf{Z}}$ fundamental groups. Corollaries. concern the homotopy groups of the group $ {\text{TOP}}(M)$ of self-homeomorphisms of $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0735551-4
Article copyright: © Copyright 1984 American Mathematical Society