Hilden, Hugh MichaelLozano Imízcoz, María TeresaMontesinos Amilibia, José María2023-06-202023-06-2020050166-864110.1016/j.topol.2004.11.017https://hdl.handle.net/20.500.14352/50759If K is a hyperbolic knot in S3, an algebraic component of its character variety containing one holonomy of the complete hyperbolic structure of finite volume of S3∖K is an algebraic curve K. The traces of the peripheral elements of K define polynomial functions in K, which are related in pairs by polynomials (peripheral polynomials). These are determined by just two adjacent peripheral polynomials. The curves defined by the peripheral polynomials are all birationally equivalent to K, with only one possible exception. The canonical peripheral polynomial relating the trace of the meridian with the trace of the canonical longitude of K is a factor of the A-polynomial.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0166864104003840http://www.journals.elsevier.com/topology-and-its-applications/restricted access5151.1Character varietyHyperbolic knotGeometria algebraicaTopología1201.01 Geometría Algebraica1210 Topología