Filtrations on the knot contact homology of transverse knots

We construct a new invariant of transverse links in the standard contact structure on ℝ3 This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link, see (Ekholm et al., Knot contact homology, Arxiv:1109. 1542, 2011; Ng, Duke Math J 141(2):365-406, 2008). Here the knot contact homology of a link in ℝ3 is the Legendrian contact homology DGA of its conormal lift into the unit cotangent bundle S*ℝ3 of ℝ3, and the filtrations are constructed by counting intersections of the holomorphic disks of the DGA differential with two conormal lifts of the contact structure. We also present a combinatorial formula for the filtered DGA in terms of braid representatives of transverse links and apply it to show that the new invariant is independent of previously known invariants of transverse links. © 2012 Springer-Verlag.

Duke Scholars

Author Lenhard Lee Ng Mathematics