Resumen de Thin position for knots in a 3-manifold

Maggy Tomova

• 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.