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.

Notes on file formats

Selman Akbulut
Department of Mathematics
Michigan State University
MI, 48824, USA
Email: akbulut@math.msu.edu

GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.