A spectrum connecting the braid index and the bridge index

Margaret Doig; Chase Gehringer

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arXiv · 2411.09845

A spectrum connecting the braid index and the bridge index

Margaret Doig·Chase Gehringer

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Abstract

We study the booklink, a braid-like embedding with local maxima and minima, and the bridge-braid spectrum of a link, which captures the smallest number of braid-strands in a booklink with a prescribed number of critical points. This spectrum spans the gap between the classical bridge and braid indices. We apply a foliation theory argument to provide a formula for the spectra of both split and composite links. We then generate a table for the spectra of all prime knots up to 9 crossings.

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Margaret Doig, Chase Gehringer. 2024-11-14. A spectrum connecting the braid index and the bridge index. https://arxiv.org/abs/2411.09845

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