#### Volume 6, issue 1 (2002)

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Cappell–Shaneson's $4$–dimensional $s$–cobordism

### Selman Akbulut

Geometry & Topology 6 (2002) 425–494
 arXiv: math.GT/0208092
##### Abstract

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.

##### Keywords
$s$–cobordism, quaternionic space
##### Mathematical Subject Classification 2000
Primary: 57R55, 57R65
Secondary: 57R17, 57M50