Manifolds Obtained by Surgery on Infinitely Many Distinct Knots
by
John Osoinach
The University of Texas at Austin

We describe a method of constructing infinite sets of distinct hyperbolic knots in S³ each of which admit a surgery yielding the same manifold. In one case, the resulting closed manifold is hyperbolic; in another, the resulting closed manifold is toroidal. Furthermore, in the latter case the manifold constructed has a unique essential torus, and there is no bound on the number of times the cores of the attached solid tori puncture this torus.

Date received: February 6, 1998