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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María
(1992)
*The arithmeticity of the figure eight knot orbifolds.*
In
Topology '90.
Ohio State University Mathematical Research Institute Publications
(1).
Walter de Gruyter & Co, Berlin, pp. 169-183.
ISBN 3-11-012598-6

## Abstract

Continuing their investigation [in Topology '90 (Columbus, OH, 1990), 133–167, de Gruyter, Berlin, 1992;] of the problem of how rarely a hyperbolic orbifold is arithmetic, the authors classify the arithmetic figure eight orbifolds: there are exactly six among the hyperbolic figure eight orbifolds (K,n), n>3. This relies on work by H. Helling, A. C. Kim and J. L. Mennicke ["On Fibonacci groups'', Preprint; per bibl.] and extends a recent result of A. Reid [J. London Math. Soc. (2) 43 (1991), no. 1, 171–184;] that (K,∞) is the only arithmetic knot complement.

Item Type: | Book Section |
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Additional Information: | Papers from the Research Semester in Low-dimensional Topology held at Ohio State University, Columbus, Ohio, February–June 1990. |

Uncontrolled Keywords: | n-fold cyclic covering of the figure eight knot; figure-eight knot; orbifold; arithmetic |

Subjects: | Sciences > Mathematics > Algebraic geometry Sciences > Mathematics > Topology |

ID Code: | 22139 |

Deposited On: | 27 Jun 2013 16:56 |

Last Modified: | 12 Dec 2018 15:13 |

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