Higher Whitehead groups of certain bundles over Seifert manifolds Journal Articles

Vanishing results for W h j ( π 1 M ) ⊗ R ( R = Z , Q ,  or  Z [ 1 / 2 ] ) {\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 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- Z {\mathbf {Z}} fundamental groups. Corollaries. concern the homotopy groups of the group TOP ( M ) {\text {TOP}}(M) of self-homeomorphisms of M M .