Communications in Analysis and Geometry

Volume 24 (2016)

Number 5

Augmentation rank of satellites with braid pattern

Pages: 939 – 967



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

David R. Hemminger


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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