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.

Received 28 May 2015

Accepted 30 September 2016

Published 28 November 2017