The ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot

We describe a procedure for computing the ${\rm SL}(2,\mathbb{C})$-character variety of an arborescent knot.

Along the way, we clarify several facts about representations of arborescent tangles.

Then we study a family of hyperbolic knots whose exteriors contain closed essential surfaces, showing that each of these knots has $1$-dimensional character variety.

This provides infinitely many positive answers to a question of Boyer and Zhang posed in 1998.