Trace-free $\mathrm{SL}(2,\mathbb{C})$-representations of arborescent links

Abstract

Given a link $L\subset S^3$, a representation ${\pi }_1(S^3-L)\to \mathrm{SL}(2,\mathbb{C})$ is {\it trace-free} if it sends each meridian to an element with trace zero. We present a method for completely determining trace-free $\mathrm{SL}(2,\mathbb{C})$-representations for arborescent links. Concrete computations are done for a class of 3-bridge arborescent links.

19 pages, 8 figures; to appear on Periodica Mathematica Hungarica

References in corpus (1)

• Tracefree $\mathrm{SL}(2,\mathbb{C})$-representations of Montesinos links