Corrigendum to: Smooth nontrivial 4-dimensional $s$-cobordisms

Sylvain E. Cappell, Julius L. Shaneson
1987 Bulletin of the American Mathematical Society  
In [1] we constructed a family of nontrivial topological s-cobordisms of 3dimensional quatemionic spaces. This and further considerations led to the result that there are either 2 2r~~r~~1 or 2 2r-r distinct s-cobordisms of any quatemionic space-form M r = S 3 /Q r to itself, where Q r denotes the quaternion group of order 2 r+2 . In [2] we erroneously claimed, using in part various exact sequences in algebraic L-theory, that the upper bound was precise, and used this to detect the topological
more » ... ct the topological nontriviality of some explicitly constructed smooth s-cobordisms. Reconsideration of this material using some exact sequences of Ranicki [4] and particularly the related unpublished work on algebraic "visible" //-theory of Michael Weiss [5] leads to the opposite conclusion: THEOREM. There are precisely 2 2r~r~1 topologically distinct s-cobordisms of the quatemionic space M? to itself. In particular, the questions of whether the construction of [2] is smoothly a product, as well as the smoothability of the above examples, remain open. The above theorem will be proved in [3].
doi:10.1090/s0273-0979-1987-15616-3 fatcat:2srjmweiffamxm3zocyo4vjnzm