Matt Hedden
MIT
An invariant of knots in a contact manifold
Abstract: I'll discuss a generalization of the Ozsvath-Szabo concordance invariant which assigns a number to a knot in a three-manifold eqwuipped with a contact structure. Under favorable circumstances, this number provides upper bounds for the Thurston-Bennequin and ratation numbers of Legendrian representatives of the topological knot type in the chosen contact structure. Other applications of this invariant appear to include an interaction with the geometry of compl,ex (resp. J-holomorphic) curves in stein (resp. symplectic) fillings of the given contact manifold, detection of fibered knots which induce tight contact structures, and invariants of link concordance.