On the character variety of group representations of a 2-bridge link p/3 into PSL(2,C)

Abstract

Consider the group G of a classical knot or link in S3. It is natural to consider the representations of G into PSL(2,C). The set of conjugacy classes of nonabelian representations is a closed algebraic set called the character variety (of representations of G into PSL(2,C)). If G is the group of a 2-bridge knot or link, then a polynomial results by an earlier published theorem of the authors. This polynomial is related to the Morgan-Voyce polynomials Bn(z), which can be defined by the formulas pn(z)=Bn(z−2), where pn=zpn−1−pn−2, p0=1, p1=z, or (z1−10)n=(pnpn−1−pn−1−pn−2). In this paper the authors do many calculations for classes of 2-bridge knots or links.