Exceptional surgeries on components of 2-bridge links (Q444121)

An \textit{exceptional surgery} on a component of a 2-component hyperbolic link \(L \subset S^3\) is one that yields a knot whose complement does not admit a hyperbolic structure. Equivalently, such a surgery will produce a knot that contains an essential disk, 2-sphere, annulus, or torus in its complement. In the present paper, the author gives a precise classification of all exceptional surgeries on a component of a 2-bridge link. In particular, the author finds that such an exceptional surgery will never produce an essential disk or 2-sphere. A torus may be produced for an explicitly described set of slopes, and in these cases the knot complement that is produced will not be Seifert-fibered. When there is no essential torus there may be an essential annulus for another set of explicitly described slopes.