Manifolds obtained by surgery on an infinite number of knots in \(S^{3}\) (Q2498021)

The construction of 3-manifolds via Dehn surgery on links in \(S^3\) is an important technique in the classification of 3-manifolds. In this paper the author gives an answer to the question whether there exist 3-manifolds that can be obtained by 0-surgery on an infinite number of distinct knots in \(S^3\). He describes a method of constructing infinite collections of distinct hyperbolic knots in \(S^3\) which admit a longitudinal surgery yielding the same manifold. Using the technique presented in the paper the author describes two families of knots: in one case the knots constructed each admit a longitudinal surgery yielding the same hyperbolic manifold, in the other case the knots admit a longitudinal surgery yielding the same toroidal manifold.