COMMENSURABILITY CLASSES OF TWIST KNOTS

Abstract

In this paper we prove that if M K is the complement of a non-fibered twist knot K in [Formula: see text], 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.