9/30/2010

Josh Greene
ColumbiaUniversity

The lens space realization problem

I will discuss the classification of the which spaces arise by integral Dehn surgery along a knot in the three-sphere. A related result is that if surgery along a knot produces a connected sum of lens spaces, then the knot is either a torus knot or a cable thereof, confirming the cabling conjecture in this case. The proofs rely on Floer homology and lattice theory.