Manifolds obtained by surgery on an infinite number of knots in [formula omitted

Abstract

The construction of 3-manifolds via Dehn surgery on links in S 3 is an important technique in the classification of 3-manifolds. This paper describes a method of constructing infinite collections of distinct hyperbolic knots in S 3 which admit a longitudinal surgery yielding the same manifold. In one case, the knots constructed each admit a longitudinal surgery yielding the same hyperbolic manifold; in another case, the knots admit a longitudinal surgery yielding the same toroidal manifold. This answers a question formulated by Kirby in the Kirby problem list [R. Kirby (Ed.), Problems in low-dimensional topology, in: Geometric Topology, American Mathematical Society/International Press, 1997] in the affirmative, which asks if there is a homology 3-sphere, or any 3-manifold, that can be obtained by n surgery on an infinite number of distinct knots.