Higher Whitehead groups of certain bundles over Seifert manifolds

Nicas, A. J.; Stark, C. W.

doi:10.1090/S0002-9939-1984-0735551-4

Higher Whitehead groups of certain bundles over Seifert manifolds
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by A. J. Nicas and C. W. Stark

Proc. Amer. Math. Soc. 91 (1984), 1-5

DOI: https://doi.org/10.1090/S0002-9939-1984-0735551-4

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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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