Hyperbolic Volume and Twisted Alexander invariants of Knots and Links

Abstract

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 $t=-1$.

21 pages, 2 figures, A hypothesis in a proposition is removed

References in corpus (1)

• Reidemeister torsion, hyperbolic three-manifolds, and character varieties