The size of triangulations supporting a given link

Abstract

Let T be a triangulation of S^3 containing a link L in its 1-skeleton. We give an explicit lower bound for the number of tetrahedra of T in terms of the bridge number of L. Our proof is based on the theory of almost normal surfaces.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper13.abs.htm