Cappell–Shaneson’s 4–dimensional s–cobordism

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

References

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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

Volume 6, issue 1 (2002)

Selman Akbulut