3 papers
math.GT2025
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…
math.GT2025
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…
math.GT2025
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…