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We give a combinatorial treatment of transverse homology, a new invariant oftransverse knots that is an extension of knot contact homology. The theorycomes in several flavors, including one that is an invariant of topologicalknots and produces a three-variable knot polynomial related to theA-polynomial. We provide a number of computations of transverse homology thatdemonstrate its effectiveness in distinguishing transverse knots, includingknots that cannot be distinguished by the Heegaard Floer transverse invariantsor other previous invariants.

Combinatorial knot contact homology and transverse knots