Perturbed Alexander Invariants via Quantum Cluster Algebras

We derive a perturbative expansion of knot invariants using quantum cluster algebras. In a recent series of papers, it has been shown that the universal $R$-matrix of $U_q(\mathfrak{g})$, with $\mathfrak{g}$ a Lie algebra of type ADE, can be interpreted as a cluster transformation. For $\mathfrak{g}