The character variety of a class of rational links

Let Gn be the fundamental group of the exterior of the rational link C(2n) in Conway’s normal form, see[7]. A presentation for Gn is given by a, b | (ab)^n = (ba)^n [3, Thm. 2.2]. We study the character variety in SL(2, C ) of the group Gn . In particular, we give the defining polynomial of the character variety of Gn . As an application, we show a well-known result that Gn and Gm are isomorphic only when n = m. Also as a consequence of the main theorem of this paper, we give a basis of the Kauffman bracket skein module of the exterior of the rational link C(2n) modulo its (A +1)-torsion.