4 papers
An Alexander Polynomial Refinement for Alternating Links, with Trapezoidal Properties
Joe Boninger
We define an invariant of alternating links---a homogeneous, four-variable Laurent polynomial---that encodes the symmetrized Alexander polynomial, the signature, and other topologi…
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…
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…