Knots, Heegaard Floer Homology and Contact Geometry

Geometry Topology Seminar
Friday, November 5, 2010 - 14:00
2 hours
Skiles 171

The talk is 1.5-2 hours long, and although some knowledge of HeegaardFloer homology and contact manifolds is useful I will spend some time inthe begining to review the basic notions. So the talk should be accessibleto everyone. 

The first hour of this talk gives a gentle introduction to yet another version of Heegaard Floer homology; Sutured Floer homology. This is the generalization of Heegaard Floer homology, for 3-manifolds with decorations (sutures) on their boundary. Sutures come naturally for contact 3-manifolds. Later we will concentrate on invariants for contact 3--manifolds in Heegaard Floer homology. This can be defined both for closed 3--manifolds, in this case they live in Heegaard Floer homology and for 3--manifolds with boundary, when the invariant is in sutured Floer homology. There are two natural generalizations of these invariants for Legendrain knots. One can directly generalize the definition of the contact invariant $\widehat{\mathcal{L}}$, or one can take the complement of the knot, and compute the invariant for that:$\textrm{EH}$. At the end of this talk I would like to describe a map that sends $\textrm{EH}$ to$\widehat{\mathcal{L}}$. This is a joint work with Andr\'as Stipsicz.