Bridge numbers of knots in the page of an open book

R. Sean Bowman; Jesse Johnson

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arXiv · 1502.04228

Bridge numbers of knots in the page of an open book

R. Sean Bowman·Jesse Johnson

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Abstract

Given any closed, connected, orientable $3$--manifold and integers $g\geq g(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridge number is greater than $D$. These knots lie in a page of an open book decomposition of $M$, and the proof proceeds by examining the action of the map induced by the monodromy on the arc and curve complex of a page. A corollary is that there are Berge knots of arbitrarily large genus one bridge number.

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BibTeX RIS

R. Sean Bowman, Jesse Johnson. 2015-02-14. Bridge numbers of knots in the page of an open book. https://arxiv.org/abs/1502.04228

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