What is Heegaard Floer homology?

Series: 
Research Horizons Seminar
Wednesday, April 12, 2017 - 12:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
Georgia Tech
Organizer: 
Defined in the early 2000's by Ozsvath and Szabo, Heegaard Floer homology is a package of invariants for three-manifolds, as well as knots inside of them. In this talk, we will describe how work from Poul Heegaard's 1898 PhD thesis, namely the idea of a Heegaard splitting, relates to the definition of this invariant. We will also provide examples of the kinds of questions that Heegaard Floer homology can answer. These ideas will be the subject of the topics course that I am teaching in Fall 2017.