Duke Mathematical Journal

Framed knot contact homology

Lenhard Ng

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Abstract

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

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

Dates
First available in Project Euclid: 17 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1200601795

Digital Object Identifier
doi:10.1215/S0012-7094-08-14125-0

Mathematical Reviews number (MathSciNet)
MR2376818

Zentralblatt MATH identifier
1145.57010

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

Citation

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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