Geometry & Topology, Vol. 6 (2002) Paper no. 16, pages 425--494.

Cappell-Shaneson's 4-dimensional s-cobordism

Selman Akbulut

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

AMS subject classification. Primary: 57R55, 57R65. Secondary: 57R17, 57M50.

DOI: 10.2140/gt.2002.6.425

E-print: arXiv:math.GT/0208092

Submitted to GT on 4 September 2002. Paper accepted 2 October 2002. Paper published 23 October 2002.

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Selman Akbulut
Department of Mathematics
Michigan State University
MI, 48824, USA

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