Twist spinning of knots and metabolizers of Blanchfield pairings

Friedl, Stefan; Orson, Patrick

Abstract

In a classic paper Zeeman introduced the $k$-twist spin of a knot $K$ and showed that the exterior of a twist spin fibers over $S^1$. In particular this result shows that the knot $K\#-K$ is doubly slice. In this paper we give a quick proof of Zeeman’s result. The $k$-twist spin of $K$ also gives rise to two metabolizers for $K\#-K$ and we determine these two metabolizers precisely.

Citation

Friedl, S., & Orson, P. (2015). Twist spinning of knots and metabolizers of Blanchfield pairings. Annales de la Faculté des sciences de Toulouse (En ligne), 24(5), 1203-1218. https://doi.org/10.5802/afst.1481

• Journal Article Type: Article
• Acceptance Date: Oct 24, 2014
• Publication Date: Jan 1, 2015
• Deposit Date: Apr 27, 2015
• Publicly Available Date: Oct 1, 2018
• Journal: Annales de la Faculté des Sciences de Toulouse : Mathématiques
• Print ISSN: 0240-2963
• Electronic ISSN: 2258-7519
• Publisher: Université Paul Sabatier
• Peer Reviewed: Peer Reviewed
• Volume: 24
• Issue: 5
• Pages: 1203-1218
• DOI: https://doi.org/10.5802/afst.1481
• Public URL: https://durham-repository.worktribe.com/output/1406633
• Related Public URLs: http://arxiv.org/abs/1312.1934