We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial. We provide a number of computations of transverse homology that demonstrate its effectiveness in distinguishing transverse knots, including knots that cannot be distinguished by the Heegaard Floer transverse invariants or other previous invariants. © 2011 Elsevier Inc.
Ng, L. (2011). Combinatorial knot contact homology and transverse knots. Advances in Mathematics, 227(6), 2189–2219. https://doi.org/10.1016/j.aim.2011.04.014