The equivalence of transverse link invariants in knot Floer homology
David Shea Vela-Vick (Columbia)
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.