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. 

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