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Hilden, Hugh Michael and Lozano Imízcoz, María Teresa and Montesinos Amilibia, José María
(1995)
*On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant.*
Journal of Knot Theory and Its Ramifications, 4
(1).
pp. 81-114.
ISSN 0218-2165

Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0218216595000053

## Abstract

Let (p/q,n) be the 3-orbifold with base S3 and singular set the 2-bridge knot determined by the rational number p/q, with p and q odd and co-prime, and with cone angle 2π/n along the knot. In this paper the authors are interested in when the orbifolds (p/q,n) are hyperbolic and arithmetic. Using characterization theorems for identifying arithmetic Kleinian groups, the authors develop an algorithmic method for determining when the orbifolds (p/q,n) are arithmetic. This is achieved by using the special recursive nature for the presentation of a 2-bridge knot group to construct the representation variety for the fundamental group of the underlying 2-bridge knot. The same argument applies to 2-bridge links with the same cone angle along each component.

Item Type: | Article |
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Uncontrolled Keywords: | orbifold; singular set; two bridge knot; algebraic curve; knot invariant |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 22198 |

Deposited On: | 03 Jul 2013 17:27 |

Last Modified: | 12 Dec 2018 15:13 |

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