On tunnel number one links with surgeries yielding the 3-sphere

Abstract

Gordon and Luecke showed that knots are determined by their complements. Therefore a non-trivial Dehn surgery on a non-trivial knot does not yield the 3-sphere. But the situation for links is different from that for knots. Berge constructed some examples of Dehn surgeries of 2-component links yielding the 3-sphere with interesting properties. By extending Berge's example, we construct infinitely many examples of tunnel number one links in the 3-sphere, such that their components are non-trivial, and that non-trivial Dehn surgeries on them yield the 3-sphere.