2 citations · 4 across the 9 of their papers we have counts for
9 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…
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 an…
Special Alternating Knots are Band Prime
Joe Boninger, Joshua Evan Greene
We prove that a special alternating knot does not decompose as a non-trivial band sum. This restricts concordances from special alternating knots, and we conjecture that special al…
On the Cosmetic Crossing Conjecture for Special Alternating Links
Joe Boninger
We prove that a family of links, which includes all special alternating knots, does not admit non-nugatory crossing changes which preserve the isotopy type of the link. Our proof i…
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…
A Quantum Invariant of Links in with Volume Conjecture Behavior
Joe Boninger
We define a polynomial invariant of links in the thickened torus. We call the th toroidal colored Jones polynomial, and show it satisfies many properties of the…