Title: Hidden symmetries and cyclic commensurability for small knot complements
Abstract: Two hyperbolic orbifolds are commensurable if they share a common finite sheeted cover. Commensurability forms an equivalence relation on the set of hyperbolic orbifolds. Conjecturally, there are only three knot complements in a given commensurability class. Furthermore, if two knot complements are commensurable, Boileau, Boyer, Cebanu, and Walsh show that they are either cyclically commensurable, ie cover an orbifold with multiple finite cyclic fillings or they admit hidden symmetries, ie they cover an orbifold with a rigid cusp. After providing some of the necessary background, I will show that small, cyclically commensurable knot complements do not admit hidden symmetries.