Hilden, Hugh MichaelLozano Imízcoz, María TeresaMontesinos Amilibia, José María2023-06-202023-06-2019950218-216510.1142/S0218216595000053https://hdl.handle.net/20.500.14352/58634Let (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.journal articlehttp://www.worldscientific.com/doi/abs/10.1142/S0218216595000053http://www.worldscientific.com/metadata only access515.1orbifoldsingular settwo bridge knotalgebraic curveknot invariantTopología1210 Topología