GGT seminar: Injectivity and surjectivity of Dehn surgery

Dehn surgery (with fixed slope p/q) can be thought of as a function from the set of knots in the 3-sphere to the set of closed oriented 3-manifolds with first homology Z/p.  In 1978 Gordon conjectured that this function is never surjective or injective. Gordon-Luecke proved the surjectivity assertion in 1989. In this talk I will describe joint work with Hayden and Wakelin proving the injectivity assertion. I will also discuss some refined surjectivity and injectivity questions.