Cappell-Shaneson's 4-dimensional s-cobordism

In 1987 S Cappell and J Shaneson constructed an s-cobordism H from the quaternionic 3-manifold Q to itself, and asked whether H or any of its covers are trivial product cobordism? In this paper we study H, and in particular show that its 8-fold cover is the product cobordism from S^3 to itself. We reduce the triviality of H to a question about the 3-twist spun trefoil knot in S^4, and also relate this to a question about a Fintushel-Stern knot surgery.