Combinatorial knot contact homology and transverse knots

Details Combinatorial knot contact homology and transverse knots Combinatorial knot contact homology and transverse knots

2010-10-03

arxiv.org/abs/1010.0451v2

Adv. Math. 227 (2011), no. 6, 2189--2219

Mathematics

Symplectic Geometry

v2: 34 pages, minor corrections suggested by referee

Scientific paper

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.

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