Let G_n be the fundamental group of the exterior of the rational link C(2n) in Conway's normal form, see . A presentation for G_n is given by \langle a, b (ab)^n = (ba)^n\rangle [3, Thm. 2.2]. We study the character variety in SL(2, C) of the group G_n. In particular, we give the defining polynomial of the character variety of G_n. As an application, we show a well-known result that G_n and G_m 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.
Link group, character variety, SL_2(C) representations, Kauffman bracket skein module
"The character variety of a class of rational links,"
Turkish Journal of Mathematics: Vol. 36:
1, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol36/iss1/3