CHARACTER VARIETIES AND PERIPHERAL POLYNOMIALS OF A CLAS OF KNOTS Universidad de Zaragoza CHARACTER VARIETIES AND PERIPHERAL POLYNOMIALS OF A CLASS OF KNOTS

For a hyperbolic knot, the excellent curve is the component of the character variety containing the complete hyperbolic structure on the complement of the knot. In this paper we introduce the concept of net presentation of a knot with 2n strings which generalises the well known plat presentation of a knot with 2n strings. Nets with 4 strings are the correct setting to apply quaternion methods to compute their excellent curve. This is done here in a convenient way for application to the study of invariants of cone-manifold structures.