New formulas for the character varieties of two-bridge links

We consider some families of two-bridge links, including the links b(2p; 3), the twisted Whitehead links and the double twist links, and calculate their character varieties. Then we give simple geometrical descriptions of such varieties, and determine the number of their irreducible components. Our paper relates to the nice work of Hilden, Lozano and Montesinos on the character variety of a class of 2-bridge links, but uses very dierent methods based on the concept of palindome presentations of link groups. The obtained formulas for the above character varieties are new, easily programmable, and more simple in many cases than the equations known in the literature.