Peripheral polynomials of hyperbolic knots (Q1779527)

Let \(K\) be a hyperbolic knot in the oriented 3-sphere. Let \(X(K)\) be the character variety of representations of \(\pi_1(S^3\setminus K)\) into \(\text{SL}(2,\mathbb{C})\). A component of \(X(K)\) containing one holonomy of the complete hyperbolic structure of finite volume on \(S^3\setminus K\) is an algebraic curve. The paper is devoted to the study of this curve and of a family of associated polynomials.