Detecting essential surfaces as intersections in the character variety (Q2409811)

As it is well known, the \(SL_2\mathbb{C}\) character variety of the fundamental group of a hyperbolic \(3\)-manifold carries a lot of topological information. In particular, one can detect embedded essential surfaces in these manifolds by considering ideal points in the \(SL_2\mathbb{C}\) character variety. It may occur that such points arise from the intersection of the components of the character variety. In this paper, the author describes a family of two-bridge knots having two distinct algebraic curve components of irreducible representations in their character varieties and whose intersection points detect a Seifert surface.