Knots with only two strict essential surfaces

Details Knots with only two strict essential surfaces Knots with only two strict essential surfaces

2004-04-09

arxiv.org/abs/math/0404195v2

Geom. Topol. Monogr. 7 (2004) 335-430

Mathematics

Geometric Topology

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper14.abs.html

Scientific paper

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.

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