Vol. 38, No. 3, 1971

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Elementary surgery along a torus knot

Louise Elizabeth Moser

Vol. 38 (1971), No. 3, 737–745

In this paper a classification of the manifolds obtained by a (p,q) surgery along an (r,s) lorus knot is given. If |σ| = |rsp + q|0, then the manifold is a Seifert manifold, singularly fibered by simple closed curves over the 2-sphere with singularities of types α1 = s,α2 = r, and α8 = |σ|. If |σ| = 1, then there are only two singular fibers of types α1 = s,α2 = r, and the manifold is a lens space L(|q|,ps2). If |σ| = 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.

Mathematical Subject Classification
Primary: 55F55
Secondary: 57C45
Received: 19 October 1970
Published: 1 September 1971
Louise Elizabeth Moser