Hidden Symmetries and Commensurability of 2-bridge link complements.

The canonical triangulations and symmetry groups of 2-bridge link complements are well understood and relatively easy to describe. We leverage this fact to show that non-arithmetic 2-bridge link complements have no hidden symmetries (i.e., symmetries of a finite cover that do not descend to symmetries of the link complement itself), and are pairwise incommensurable. Much of the talk will focus on background material, starting with the definition of cusped hyperbolic 3-manifolds, and then commensurability, hidden symmetries, and canonical (Delaunay) triangulations. With this background material in hand, we will then give a rough sketch of our proof that 2-bridge links have no hidden symmetries. This is joint work with Christian Millichap.