Tao Su

We give a tangle approach in the study of Legendrian knots in the contact three-space. This includes Legendrian isotopy invariants: ruling polynomials, and Chekanov-Eliashberg/Legendrian Contact Homology differential graded algebras (LCH DGAs) for Legendrian tangles, generalizing those of Legendrian knots.

By studying the "(rank 1) representation varieties" of the LCH DGAs, called augmentation varieties, we also see that their point-countings/E-polynomials are given the ruling polynomials. The tangle approach in particular provides a more natural proof to some previous known results of M.Henry and D.Rutherford. Time permitting, I will also mention some more aspects of the study of augmentation varieties.