Augmentation Rank of Satellites with Braid Pattern

Christopher R. Cornwell; David R. Hemminger

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arXiv · 1408.4110

Augmentation Rank of Satellites with Braid Pattern

Christopher R. Cornwell·David R. Hemminger

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Abstract

Given a knot $K$ in $S^3$, a question raised by Cappell and Shaneson asks if the meridional rank of $K$ equals the bridge number of $K$. Using augmentations in knot contact homology we consider the persistence of equality between these two invariants under satellite operations on $K$ with a braid pattern. In particular, we answer the question in the affirmative for a large class of iterated torus knots.

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BibTeX RIS

Christopher R. Cornwell, David R. Hemminger. 2014-08-18. Augmentation Rank of Satellites with Braid Pattern. https://arxiv.org/abs/1408.4110

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