Remarks on some hyperbolic invariants of 2-bridge knots

In this paper we describe a recursive technique that can be used to investigate a number of hyperbolic invariants of certain classes of 2-bridge knots. We explicitly compute the representation and character varieties, the trace and cusp fields, and A-polynomials for these knots. Using these computations we obtain information about these knots' commensurability classes. Experimental results lead naturally to two conjectures regarding trace fields and commensurability classes of 2-bridge knots. We conclude with a discussion of a result of Hodgson which generalizes other results of this paper.