27 citations · 61 across the 8 of their papers we have counts for
6 papers · 1 filter
Character varieties of knot complements and branched double-covers via the cord ring
Christopher R. Cornwell
We study the relationship between Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover . Augmentations, and their corresponding rank, play a central r…
Berge duals and universally tight contact structures
Christopher R. Cornwell
Dehn surgery on a knot determines a dual knot in the surgered manifold, the core of the filling torus. We consider duals of knots in that have a lens space surgery. Each dual…
Augmentation Rank of Satellites with Braid Pattern
Christopher R. Cornwell, David R. Hemminger
Given a knot in , a question raised by Cappell and Shaneson asks if the meridional rank of equals the bridge number of . Using augmentations in knot contact homolog…
KCH representations, augmentations, and -polynomials
Christopher Cornwell
We describe a correspondence between augmentations and certain representations of the knot group. The correspondence makes the 2-variable augmentation polynomial into a generalizat…
Bennequin type inequalities in lens spaces
Christopher R. Cornwell
We give criteria for an invariant of lens space links to bound the maximal self-linking number in certain tight contact lens spaces. As a corollary we extend the Franks-Williams-Mo…
A polynomial invariant for links in lens spaces
Christopher Cornwell
We prove the existence of a polynomial invariant that satisfies the HOMFLY skein relation for links in a lens space. In the process we also develop a skein theory of toroidal grid…