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.
Department of Mathematics
College of Liberal Arts & Sciences
273 Altgeld Hall
1409 W. Green Street (MC-382)
Urbana, IL 61801
Telephone: 217-333-3350
Email: math@illinois.edu