KCH representations, augmentations, and $A$-polynomials

Christopher Cornwell

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arXiv · 1310.7526

KCH representations, augmentations, and $A$-polynomials

Christopher Cornwell

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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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Christopher Cornwell. 2017-06-05. KCH representations, augmentations, and $A$-polynomials. https://arxiv.org/abs/1310.7526

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