Augmentation Rank of Satellites with Braid Pattern
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.
Type
Department
Description
Provenance
Subjects
Citation
Permalink
Citation
Hemminger, David (2015). Augmentation Rank of Satellites with Braid Pattern. Honors thesis, Duke University. Retrieved from https://hdl.handle.net/10161/9741.
Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.