CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

Neil R. Hoffman

doi:10.1090/bproc/104

CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

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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, S²(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 S²(2, 3, 6) cusp, it also covers an orbifold with a S²(3, 3, 3) cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.

Original language	English (US)
Pages (from-to)	336-350
Number of pages	15
Journal	Proceedings of the American Mathematical Society, Series B
Volume	9
DOIs	https://doi.org/10.1090/bproc/104
State	Published - 2022
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2022 by the author(s).

Keywords

and phrases. Rigid cusps
commensurability
quotients of knot complements

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AB - 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, S2(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 S2(2, 3, 6) cusp, it also covers an orbifold with a S2(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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CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

Abstract

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