Bridge numbers of knots in the page of an open book

Abstract

Given any closed, connected, orientable $3$--manifold and integers $g\ge g(M),D>0$, 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.

21 pages, 2 figures

References in corpus (1)

• Bridge spectra of twisted torus knots