Georgia Institute of Technology College of Sciences

Heegaard Floer theory consists of a set of invariants of three-and four-dimensional manifolds. Three-manifolds with the simplest HeegaardFloer invariants are called L-spaces and the name stems from the fact thatlens spaces are L-spaces. The primary focus of this talk will be on thequestion of which knots in the three-sphere admit L-space surgeries. Wewill also discuss about possible characterizations of L-spaces that do notreference Heegaard Floer homology.