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math.GT2026
Perturbed-Alexander Invariants via Quantum Cluster Algebras
Boudewijn Bosch
A perturbative expansion of knot invariants is derived using quantum cluster algebras. By interpreting the -matrix of as a cluster transformation and intr…
math.GT2025
Tensors, Gaussians and the Alexander Polynomial
Boudewijn Bosch
In this paper, we formally show that the Alexander polynomial of a knot can be computed through contractions of a Gaussian function. We build on the approach of Bar-Natan and Van d…
math.GT2024
The Large-Color Expansion Derived from the Universal Invariant
Boudewijn Bosch
The colored Jones polynomial associated to a knot admits an expansion of knot invariants known as the large-color expansion or Melvin-Morton-Rozansky expansion. We will show how th…