Communications in Analysis and Geometry

Volume 24 (2016)

Number 5

Augmentation rank of satellites with braid pattern

Pages: 939 – 967

DOI: https://dx.doi.org/10.4310/CAG.2016.v24.n5.a2

Authors

Christopher R. Cornwell (Department of Mathematics, Towson University, Towson, Maryland, U.S.A.)

David R. Hemminger

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.

Published 6 March 2017