The Character Varieties of Rational Links C(2n, 2m + 1, 2)

In this thesis we study the nonabelian SL2(C) character varieties of an infinite family of rational links. In chapter 1 we provide background information on rational knots and links and their character varieties. We also provide some properties of Chebyshev polynomials, which will be used in calculating the character varieties. In chapter 2 we first find a presentation for the knot group of C(2n, 2m + 1, 2). We then calculate the nonabelian character variety and prove that the character variety of C(2n, 2m + 1, 2) is irreducible unless n = 1, 1 or m = 1.