Combinatorial knot contact homology and transverse knots

Understand

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.