Kyoto Journal of Mathematics

On a relation between the self-linking number and the braid index of closed braids in open books

Tetsuya Ito

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Abstract

We prove a generalization of the Jones–Kawamuro conjecture that relates the self-linking number and the braid index of closed braids, for planar open books with certain additional conditions and modifications. We show that our result is optimal in some sense by giving several examples that do not satisfy a naive generalization of the Jones–Kawamuro conjecture.

Article information

Source
Kyoto J. Math., Volume 58, Number 1 (2018), 193-226.

Dates
Received: 25 January 2016
Revised: 25 August 2016
Accepted: 31 August 2016
First available in Project Euclid: 10 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1510283180

Digital Object Identifier
doi:10.1215/21562261-2017-0021

Mathematical Reviews number (MathSciNet)
MR3776283

Zentralblatt MATH identifier
06873132

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx] 57R17: Symplectic and contact topology

Keywords
self-linking number closed braid open book foliation Jones–Kawamuro conjecture

Citation

Ito, Tetsuya. On a relation between the self-linking number and the braid index of closed braids in open books. Kyoto J. Math. 58 (2018), no. 1, 193--226. doi:10.1215/21562261-2017-0021. https://projecteuclid.org/euclid.kjm/1510283180


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References

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