Abstract:

In contact geometry, Legendrian contact homology defines powerful and interesting Legendrian knot invariants. The definition of such an invariant is complicated, and often computations are made by defining a combinatorial analogue of the invariant. Even so, the combinatorial invariant has been defined in only a handful of contact 3-manifolds. In this talk we show how to define a combinatorial invariant for Legendrian knots that can be defined in new contact 3-manifolds where the key ingredient for this new invariant is the notion of a Morse structure on a contact 3-manifold.