Knot contact homology and representations of knot groups

Abstract

We study certain linear representations of the knot group that induce augmentations of knot contact homology. This perspective on augmentations enhances our understanding of the relationship between the augmentation polynomial and the A-polynomial of the knot. For example, we show that for 2-bridge knots the polynomials agree and that this is never the case for (non-2-bridge) torus knots, nor for a family of 3-bridge pretzel knots. In addition, we obtain a lower bound on the meridional rank of the knot. As a consequence, our results give another proof that torus knots and a family of pretzel knots have meridional rank equal to their bridge number.

revision, published in J. Topology

References in corpus (1)

• A topological introduction to knot contact homology

Cited by in corpus (6)

• The conormal torus is a complete knot invariant
• Augmentation Rank of Satellites with Braid Pattern
• Meridional rank and bridge number for a class of links
• Character varieties of knot complements and branched double-covers via the cord ring
• Simple Sheaves for Knot Conormals
• Augmentations and sheaves for links