%0 Journal Article
%T Knot complements, hidden symmetries and reflection orbifolds
%A Michel Boileau
%A Steven Boyer
%A Radu Cebanu
%A Genevieve S. Walsh
%J Mathematics
%D 2015
%I arXiv
%X In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic reflection orbifolds admit hidden symmetries, and we verify the Neumann-Reid conjecture for knots which cover small hyperbolic reflection orbifolds. We also show that a reflection orbifold covered by the complement of an AP knot is necessarily small. Thus when $K$ is an AP knot, the complement of $K$ covers a reflection orbifold exactly when $K$ is either the figure-eight knot or one of the dodecahedral knots.
%U http://arxiv.org/abs/1501.02253v1