Resumen de Thin position for knots in a 3-manifold
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.
