Cappell-Shaneson's 4-dimensional s-cobordism

Details Cappell-Shaneson's 4-dimensional s-cobordism Cappell-Shaneson's 4-dimensional s-cobordism

2002-08-12

arxiv.org/abs/math/0208092v2

Geom. Topol. 6(2002) 425-494

Mathematics

Geometric Topology

70 pages, 146 figures in colour, published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper16.abs.ht

Scientific paper

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.

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