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On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant

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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
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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