Quasi-alternating links and lens space surgeries

Josh Greene (Princeton University)

I will discuss the use of Donaldson's Theorem as an obstruction to a link being quasi-alternating. One consequence is the production of non-quasi-alternating links whose knot Floer and Khovanov invariants are thin. Then I will discuss the use of Donaldson's Theorem, in combination with some input from Heegaard Floer homology, as an obstruction to a knot having a lens space surgery. One consequence is an upper bound on the genus of such a knot in terms of the surgery coefficient, and that (im)proves a bound conjectured by Goda-Teragaito.