Marc Culler, Peter B Shalen
Published 2004-04-09, updated 2004-12-23Version 2
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.
Comments: Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper14.abs.html
Journal: Geom. Topol. Monogr. 7 (2004) 335-430
Octahedral developing of knot complement I: pseudo-hyperbolic structure
Distance of Heegaard splittings of knot complements
Octahedral developing of knot complement II: Ptolemy coordinates and applications
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