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

Abstract

Given a link L ⊂ S 3 , a representation π 1 (S 3 − L) → SL(2, C) is trace-free if it sends each meridian to an element with trace zero. We present a method for completely determining trace-free SL(2, C)representations for arborescent links. Concrete computations are done for a class of 3-bridge arborescent links.

The Sl(2, )-Character Variety of a Montesinos Knot

“…Assume that all meridians are sent to elements of trace t. The case when t = 0 has been carefully treated in [3]. In this section, we always assume t = 0.…”