Cusp types of quotients of hyperbolic knot complements

Abstract

This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, S 2 ( 2 , 4 , 4 ) S^2(2,4,4) cannot be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. Furthermore, if a knot complement covers an orbifold with a S 2 ( 2 , 3 , 6 ) S^2(2,3,6) cusp, it also covers an orbifold with a S 2 ( 3 , 3 , 3 ) S^2(3,3,3) cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.