Augmentation Rank of Satellites with Braid Pattern
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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.
CitationHemminger, David (2015). Augmentation Rank of Satellites with Braid Pattern. Honors thesis, Duke University. Retrieved from http://hdl.handle.net/10161/9741.
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Rights for Collection: Undergraduate Honors Theses and Student papers