Journal of Symplectic Geometry

Volume 15 (2017)

Number 4

KCH representations, augmentations, and $A$-polynomials

Pages: 983 – 1017



Christopher R. Cornwell (Department of Mathematics, Towson University, Towson, Maryland, U.S.A.)


We describe a correspondence between augmentations of knot contact homology and certain representations of the knot group. The correspondence makes the $2$-variable augmentation polynomial into a generalization of the classical $A$-polynomial. It also associates to an augmentation a rank, which is bounded by the bridge number and shares its behavior under connect sums. We also study augmentations with rank equal to the braid index.

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Paper received on 28 May 2015.

Paper accepted on 30 September 2016.