Framed knot contact homology

Lenhard Ng

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Framed knot contact homology

Lenhard Ng

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Abstract

We extend knot contact homology to a theory over the ring $\mathbb{Z}[λ^{\pm 1},μ^{\pm 1}]$, 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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Lenhard Ng. 2007-05-22. Framed knot contact homology. https://arxiv.org/abs/math/0407071

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