Combinatorial knot contact homology and transverse knots

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.Comment: v2: 34 pages, minor corrections suggested by refere

Conormal bundles, contact homology and knot invariants

We summarize recent work on a combinatorial knot invariant called knot contact homology. We also discuss the origins of this invariant in symplectic topology, via holomorphic curves and a conormal bundle naturally associated to the knot.Comment: This is the version published by Geometry & Topology Monographs on 22 April 200

A topological introduction to knot contact homology

This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.Comment: 38 pages, based on lectures at the Contact and Symplectic Topology Summer School in Budapest, July 2012; v2: fixed typos, updated references, version to be publishe