  The main result is that an s-cobordism (topological or smooth) of 4-manifolds
has a product structure outside a ``core'' sub s-cobordism. These cores are
arranged to have quite a bit of structure, for example they are smooth and
abstractly (forgetting boundary structure) diffeomorphic to a standard
neighborhood of a 1-complex. The decomposition is highly nonunique so cannot be
used to define an invariant, but it shows the topological s-cobordism question
reduces to the core case. The simply-connected version of the decomposition
(with 1-complex a point) is due to Curtis, Freedman, Hsiang and Stong.
Controlled surgery is used to reduce topological triviality of core
s-cobordisms to a question about controlled homotopy equivalence of
4-manifolds. There are speculations about further reductions.
