Duke Mathematical Journal

Framed knot contact homology

Lenhard Ng

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We extend knot contact homology to a theory over the ring Z[λ±1,μ±1] with the invariant given topologically and combinatorially. The improved invariant, which is defined for framed knots in S3 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 that is related to the A-polynomial

Article information

Duke Math. J., Volume 141, Number 2 (2008), 365-406.

First available in Project Euclid: 17 January 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 53D12: Lagrangian submanifolds; Maslov index 53D40: Floer homology and cohomology, symplectic aspects


Ng, Lenhard. Framed knot contact homology. Duke Math. J. 141 (2008), no. 2, 365--406. doi:10.1215/S0012-7094-08-14125-0. https://projecteuclid.org/euclid.dmj/1200601795

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