Abstract
For a hyperbolic knot, the excellent curve is the union of components of the character variety containing the characters of the complete hyperbolic structures on the complement of the knot. The peripheral polynomials define the excellent curve in terms of traces of bases of the boundary torus around 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 the excellent curve. This is done here in a convenient way for application to the study of invariants of cone-manifold structures.
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