Commensurability classes of twist knots

In this paper we prove that if M-K is the complement of a non-fibered twist knot K in S-3, then M-K is not commensurable to a fibered knot complement in a Z/2Z-homology sphere. To prove this result we derive a recursive description of the character variety of twist knots and then prove that a commensurability criterion developed by Calegari and Dunfield is satisfied for these varieties. In addition, we partially extend our results to a second infinite family of 2-bridge knots.