Journal of Symplectic Geometry

Volume 15 (2017)

Number 4

KCH representations, augmentations, and $A$-polynomials

Pages: 983 – 1017

DOI: http://dx.doi.org/10.4310/JSG.2017.v15.n4.a2

Author

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

Abstract

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.

Full Text (PDF format)

Paper received on 28 May 2015.

Paper accepted on 30 September 2016.