5 papers · 1 filter
Twisted Knots and the Perturbed Alexander Invariant
Joe Boninger
The perturbed Alexander invariant , defined by Bar-Natan and van der Veen, is a powerful, easily computable polynomial knot invariant with deep connections to the Alexander a…
Knot Floer Homology, the Burau Representation, and Quantum
Joe Boninger
The Burau representation of braid groups and knot Floer homology share a link to the Fox calculus. We make this connection explicit, with the following outcome: if is the full…
The Jones Polynomial from a Goeritz Matrix
Joe Boninger
We give an explicit algorithm for calculating the Kauffman bracket of a link diagram from a Goeritz matrix for that link. Further, we show how the Jones polynomial can be recovered…
An Alexander Polynomial Obstruction to Cosmetic Crossing Changes
Joe Boninger
The cosmetic crossing conjecture posits that switching a non-trivial crossing in a knot diagram always changes the knot type. Generalizing work of Balm, Friedl, Kalfagianni and Pow…
Positive Knots and Ribbon Concordance
Joe Boninger
Ribbon concordances between knots generalize the notion of ribbon knots. Agol, building on work of Gordon, proved ribbon concordance gives a partial order on knots in . In pre…