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

Tetsuya Ito

doi:10.1215/21562261-2017-0021

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arXiv · 1501.07314

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 counter examples for naive generalizations of the Jones-Kawamuro conjecture.

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Tetsuya Ito. 2015-01-29. On a relation between the self-linking number and the braid index of closed braids in open books. https://doi.org/10.1215/21562261-2017-0021

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