KCH representations, augmentations, and A-polynomials

2013/10/28 by Cornwell, Christopher · 1 citation
#57M27 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1310.7526

Abstract

We describe a correspondence between augmentations 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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• Knot contact homology as a planar limit of Chern-Simons theory

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