Local detection of strongly irreducible Heegaard splittings via knot exteriors

Details Local detection of strongly irreducible Heegaard splittings via knot exteriors Local detection of strongly irreducible Heegaard splittings via knot exteriors

2002-06-09

arxiv.org/abs/math/0206085v1

Mathematics

Geometric Topology

12 pages

Scientific paper

We study the way a strongly irreducible Heegaard surface $\Sigma$ intersects a knot exterior $X$ embedded in a 3-manifold, and show that if $\Sigma \cap \partial X$ consists of simple closed curves which are essential in both $\Sigma$ and $\partial X$, then the intersection $X \cap \Sigma$ consists of meridional annuli only. As an application we show that when considering two Heegaard surfaces that intersect essentially and spinally (cf. Rubinstein and Shcarlemann) any embedded torus in the union of the two bounds a solid torus.

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