Hyperbolic Volume and Twisted Alexander invariants of Knots and Links

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...

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Bibliographic Details
Main Author Goda, Hiroshi
Format Journal Article
LanguageEnglish
Published 26.10.2017
Subjects
Mathematics - Geometric Topology
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Summary: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 $t=-1$.
DOI:10.48550/arxiv.1710.09963