In this paper, we show that any non-arithmetic hyperbolic 2-bridge link
complement admits no hidden symmetries. As a corollary, we conclude that a
hyperbolic 2-bridge link complement cannot irregularly cover a hyperbolic
3-manifold. By combining this corollary with the work of Boileau and
Weidmann, we obtain a characterization of 3-manifolds with non-trivial
JSJ-decomposition and rank two fundamental groups. We also show that the only
commensurable hyperbolic 2-bridge link complements are the figure-eight knot
complement and the 622 link complement. Our work requires a careful
analysis of the tilings of R2 that come from lifting the
canonical triangulations of the cusps of hyperbolic 2-bridge link
complements.Comment: This is the final (accepted) version of this pape