CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

Neil R. Hoffman

doi:10.1090/bproc/104

CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

Neil R. Hoffman

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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

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

Keywords

and phrases. Rigid cusps
commensurability
quotients of knot complements

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10.1090/bproc/104

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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.",

keywords = "and phrases. Rigid cusps, commensurability, quotients of knot complements",

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year = "2022",

doi = "10.1090/bproc/104",

language = "English (US)",

volume = "9",

pages = "336--350",

journal = "Proceedings of the American Mathematical Society, Series B",

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T1 - CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

AU - Hoffman, Neil R.

PY - 2022

Y1 - 2022

N2 - 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.

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.

KW - and phrases. Rigid cusps

KW - commensurability

KW - quotients of knot complements

UR - https://www.scopus.com/pages/publications/85136279077

UR - https://www.scopus.com/pages/publications/85136279077#tab=citedBy

U2 - 10.1090/bproc/104

DO - 10.1090/bproc/104

M3 - Article

AN - SCOPUS:85136279077

SN - 2330-1511

VL - 9

SP - 336

EP - 350

JO - Proceedings of the American Mathematical Society, Series B

JF - Proceedings of the American Mathematical Society, Series B

ER -

CUSP TYPES OF QUOTIENTS OF HYPERBOLIC KNOT COMPLEMENTS

Abstract

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