University of Arkansas Topology Seminar: 2/20/2014

Speaker: Sean Bowman

Title: Bridge numbers of knots in the page of an open book

Abstract: An open book decomposition of a 3−manifold M consists of a binding L and a bundle map from the complement of L to the circle such that the preimage of a point of the circle is the interior of a surface S whose boundary is the link L. Such a surface is called a page of the open book, and we examine knots lying in these surfaces. By studying the action of the map on the arc and curve complex of a page induced by the bundle map, we find knots which have arbitrarily large bridge number with respect to Heegaard splittings of every genus up to minus the Euler characteristic of S. Several corollaries will be noted.