Orientable rigid cusp types covered by hyperbolic knot complements

Neil R Hoffman

Published 2020-01-14Version 1

This paper completes a classification of the types of orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, $S^2(2,4,4)$ can not be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. Furthermore, if a knot complement covers an orbifold with a $S^2(2,3,6)$ cusp, it also covers an orbifold with a $S^2(3,3,3)$ cusp. We end with a discussion of non-orientable cusps, which is also informed by the main theorems.