Thin position for knots in a 3-manifold

• Autores: Maggy Tomova
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 1, 2009, págs. 85-98
• Idioma: inglés
• DOI: 10.1112/jlms/jdp009
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• Resumen

  • We extend the notion of a thin position of a link in a 3-manifold with respect to a generalized Heegaard splitting introduced in Hayashi and Shimokawa (Pacific J. Math. 197 (2001) 301�324), to take into consideration not only compressing disks but also cut-disks for the Heegaard surfaces.

    We prove that, if P is a c-weakly reducible bridge surface for a link K contained in a closed, orientable, irreducible 3-manifold M, then one of the following is satisfied:

    � P is stabilized;

    � P is meridionally stabilized;

    � P is perturbed;

    � a component of K is removable;

    � M contains an essential meridional surface.