Structure sets vanish for certain bundles over Seifert manifolds

Christopher W. Stark
1984 Transactions of the American Mathematical Society  
Let M" + i be a compact orientable manifold which is the total space of a fiber bundle over a compact orientable manifold K3 with an effective circle action of hyperbolic type. Assume that the fiber N" in this bundle is a closed orientable manifold with Noetherian integral group ring, with vanishing projective class and Whitehead groups, and such that the structure set SJOP(N" X Dk, 3) of topological surgery vanishes for sufficiently large k. Then the projective class and Whitehead groups of M
more » ... tehead groups of M vanish and ST0P(M"+3 X Dk, 3) = 0 if n + k> 3 or if AT3 is closed and n = 2. The UNil groups of Cappell are the main obstacle here, and these results give new examples of generalized free products of groups such that UNily vanishes in spite of the failure of Cappell's sufficient condition.
doi:10.1090/s0002-9947-1984-0752493-3 fatcat:ddyr6ckxyvfzxisgsacayljdli