Let $\Delta_{ L,\rho_n}(t)$ be the twisted Alexander polynomial with respect to the representation given by the composition of the lift of the holonomy representation of a certain hyperbolic link $L$ and the $n$-dimensional irreducible complex representation of $\text{ SL}(2,\mathbb C)$. We consider a sequence of $\Delta_{ L,\rho_n}(t)$ and extract the volume of the complement of $L$ from the asymptotic behaviour of the sequence obtained by evaluating $t=1$ or $t=-1$.
Categories: math.GT