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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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 S3 to itself. We reduce the triviality of H to a question about the 3–twist spun trefoil knot in S4, 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
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Publication
Received: 4 September 2002
Accepted: 2 October 2002
Published: 23 October 2002
Proposed: Robion Kirby
Seconded: Ronald Stern, Yasha Eliashberg
Authors
Selman Akbulut
Department of Mathematics
Michigan State University
Michigan 48824
USA