2004/04/30 by Marc Culler, Peter B Shalen · 1 citation
Mathematics · #math.GT #msc:57M15 #msc:57M25 #msc:57M50
published as Geom. Topol. Monogr. 7 (2004) 335-430 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper14.abs.html
arxiv created 2004/12/23 · arxiv updated 2009/12/01
We consider irreducible 3-manifolds M that arise as knot complements in closed 3-manifolds and that contain at most two connected strict essential surfaces. The results in the paper relate the boundary slopes of the two surfaces to their genera and numbers of boundary components. Explicit quantitative relationships, with interesting asymptotic properties, are obtained in the case that M is a knot complement in a closed manifold with cyclic fundamental group.