Cusp types of quotients of hyperbolic knot complements

Hoffman, Neil

doi:10.1090/bproc/104

Cusp types of quotients of hyperbolic knot complements
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by Neil R. Hoffman HTML | PDF

Proc. Amer. Math. Soc. Ser. B 9 (2022), 336-350

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, $S^2(2,4,4)$ 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 $S^2(2,3,6)$ cusp, it also covers an orbifold with a $S^2(3,3,3)$ cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.

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