Title: The Equivalence of Transverse Link Invariants in Knot Floer Homology
Program: Symplectic and Contact Geometry and Connections to Low-Dimensional Topology
Speaker: David Shea Vela-Vick, Louisiana State University
Date: Thursday, November 15, 2012
Time: 2:00pm – 3:00pm
Place: Seminar Room 313, Simons Center
Abstract: The Heegaard Floer package provides a robust tool for studying contact 3-manifolds and their subspaces. Within the sphere of Heegaard Floer homology, several invariants of Legendrian and transverse knots have been defined. The first such invariant, constructed by Ozsvath, Szabo and Thurston, was defined combinatorially using grid diagrams. The second invariant was obtained by geometric means using open book decompositions by Lisca, Ozsvath, Stipsicz and Szabo. We show that these two previously defined invariant agree. Along the way, we define a third, equivalent Legendrian/transverse invariant which arises naturally when studying transverse knots which are braided with respect to an open book decomposition.