More 3-manifolds with multiple knot-surgery and branched-cover descriptions

For any integer N ^ 3 we will construct a 3-manifold which can be described as +1 surgery on N distinct knots in S. We will also give examples of 3-manifolds which are i^-fold cyclic branched covers of S over 2 distinct knots. Brakes (2) discovered the first examples of 3-manifolds with multiple knot surgery descriptions. Our construction is much different and follows directly from the construction used by Lickorish(6) to describe a manifold which has 2 distinct knot surgery descriptions. Giller (5) has given examples of 3-manifolds which arise as cyclic branched covers over distinct knots in S. Qur construction is similar, but the knots are much easier to distinguish, being iterated torus knots. Throughout this paper we will be working in the smooth category.