Local detection of strongly irreducible Heegaard splittings via knot exteriors

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We study the way a strongly irreducible Heegaard surface $Σ$ intersects a knot exterior $X$ embedded in a 3-manifold, and show that if $Σ\cap \partial X$ consists of simple closed curves which are essential in both $Σ$ and $\partial X$, then the intersection $X \cap Σ$ 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.
12 pages

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Geometric Topology, 57M99

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http://salesiana.dossiersoluciones.com/handle/123456789/64262

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206085
 http://arxiv.org/abs/math/0206085

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arXiv