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 \ = 1, then there are only two singular fibers of types ai = s, a 2 = r, and the manifold is a lens space L(\, 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.
No takes yet. Share an insight, caveat, or question.
Louise E. Moser (1971) studied this question.