Framed knot contact homology
Abstract
We extend knot contact homology to a theory over the ring $\mathbb{Z}[\lambda^{\pm 1},\mu^{\pm 1}]$, with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in $S^3$ and can be generalized to knots in arbitrary manifolds, distinguishes the unknot and can distinguish mutants. It contains the Alexander polynomial and naturally produces a twovariable polynomial knot invariant which is related to the $A$polynomial.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 2004
 arXiv:
 arXiv:math/0407071
 Bibcode:
 2004math......7071N
 Keywords:

 Mathematics  Geometric Topology;
 Mathematics  Symplectic Geometry;
 57M27;
 53D12;
 53D40
 EPrint:
 v3: 36 pages, minor corrections, to appear in Duke Math. J