Geometry & Topology

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

Selman Akbulut

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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.

Article information

Geom. Topol., Volume 6, Number 1 (2002), 425-494.

Received: 4 September 2002
Accepted: 2 October 2002
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R55: Differentiable structures 57R65: Surgery and handlebodies
Secondary: 57R17: Symplectic and contact topology 57M50: Geometric structures on low-dimensional manifolds

$s$–cobordism quaternionic space


Akbulut, Selman. Cappell–Shaneson's $4$–dimensional $s$–cobordism. Geom. Topol. 6 (2002), no. 1, 425--494. doi:10.2140/gt.2002.6.425.

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