TITLE: 4-dimensional h-cobordisms
QUESTION [17 upvotes]: I would like to know the state of the art concerning the following two questions.
1) Does there exist a smooth 4-dimensional h-cobordism (so between closed 3-manifolds) with non-vanishing Whitehead torsion ?
2) Does there exist a smooth 4-dimensional s-cobordism (that is, with vanishing Whitehead torsion) which is not diffeomorphic to a product cobordism ?
Thank you !

REPLY [7 votes]: The answer to question 1 is no in the orientable case .Every topological 4-dim.h-cobordism is an s-cobordism.
I think that the argument in the paper S.Kwasik,R.Schultz:Vanishing of Whitehead torsion in dimension 4,Topology,vol.31(1992),pp.735-756 should also give the non-orientable case.
The orientable case is the main theorem on p.736.It was proved for geometric 3-manifolds,but now we know that all3-manifods are geometric.