# Framed knot contact homology

@article{Ng2004FramedKC,
title={Framed knot contact homology},
author={L. Ng},
journal={Duke Mathematical Journal},
year={2004},
volume={141},
pages={365-406}
}
• L. Ng
• Published 2004
• Mathematics
• Duke Mathematical Journal
• 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 two-variable polynomial knot invariant which is related to the $A$-polynomial.