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In 1987 S Cappell and J Shaneson constructed an s-cobordism H from thequaternionic 3-manifold Q to itself, and asked whether H or any of its coversare trivial product cobordism? In this paper we study H, and in particular showthat its 8-fold cover is the product cobordism from S^3 to itself. We reducethe 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.

Cappell–Shaneson’s 4–dimensionals–cobordism