Elementary surgery along a torus knot

Abstract

In this paper a classification of the manifolds obtained by a (p, q) surgery along an (r, s) torus knot is given. If | <r [ = I rsp + q I 0, then the manifold is a Seifert manifold, singularly fibered by simple closed curves over the 2-sphere with singularities of types a = s, a 2 = r, and <x z =\\. If \a\ = 1, then there are only two singular fibers of types ai = s, a 2 = r, and the manifold is a lens space L(\q\, ps If I a1 =0, then the manifold is not singularly fibered but is the connected sum of two lens spaces L(r, s)#L(s, r). It is also shown that the torus knots are the only knots whose complements can be singularly fibered.