The character variety of some classes of rational knots

Abstract

We propose a method to determine the character variety of a class [Formula: see text] of rational knots, which includes the twist knots. The defining polynomials depend only on the variables [Formula: see text] and [Formula: see text]. This answers for these classes of knots a question posed in [H. M. Hilden, M. T. Lozano and J. M. Montesinos–Amilibia, On the character variety of group representations of a 2-bridge link [Formula: see text] into [Formula: see text], Bol. Soc. Mat. Mexicana 37(2) (1992) 241–262], and allows us to give an easy geometrical description of the considered character variety. Our results are obtained by using special presentations of the knot groups whose relators are palindromes.