Combinatorial knot contact homology and transverse knots
Symplectic Geometry
2013-05-08 v2 Geometric Topology
Abstract
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.
Keywords
Cite
@article{arxiv.1010.0451,
title = {Combinatorial knot contact homology and transverse knots},
author = {Lenhard Ng},
journal= {arXiv preprint arXiv:1010.0451},
year = {2013}
}
Comments
v2: 34 pages, minor corrections suggested by referee