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arXiv · 1710.09963

Hyperbolic Volume and Twisted Alexander invariants of Knots and Links

Hiroshi Goda
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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 $t=-1$.

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Hiroshi Goda. 2017-10-27. Hyperbolic Volume and Twisted Alexander invariants of Knots and Links. https://arxiv.org/abs/1710.09963

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