English

KCH representations, augmentations, and $A$-polynomials

Geometric Topology 2017-06-07 v3

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 AA-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.

Keywords

Cite

@article{arxiv.1310.7526,
  title  = {KCH representations, augmentations, and $A$-polynomials},
  author = {Christopher Cornwell},
  journal= {arXiv preprint arXiv:1310.7526},
  year   = {2017}
}

Comments

Revised published version, 23 pages

R2 v1 2026-06-22T01:55:43.525Z