Topology Seminar (Introductory Talk): Dehn surgery, lattice theory, and Heegaard Floer homology

Seminar | September 13 | 2-3 p.m. | 740 Evans Hall

 Faramarz Vafaee, Caltech

 Department of Mathematics

I will talk about the main idea used for the work that will be presented in the second hour. I will discuss how (essentially) the same idea has been used a) to solve the lens space realization problem (by Greene) and b) to prove the conjecture that if an alternating knot has unknotting number one, then there exists an unknotting crossing in any alternating diagram (by McCoy). The idea is built primarily on the use of the d-invariants in Heegaard Floer homology in tandem with Donaldson's Theorem A. If time allows, I will propose a few questions that may be attacked using similar techniques.