%0 Journal Article
%A Hilden, Hugh Michael
%A Lozano Imízcoz, María Teresa
%A Montesinos Amilibia, José María
%T On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant
%D 1995
%@ 0218-2165
%U https://hdl.handle.net/20.500.14352/58634
%X 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.
%~