%0 Journal Article
%A Hilden, Hugh Michael
%A Montesinos Amilibia, José María
%A Tejada Jiménez, Débora María
%A Toro Villegas, Margarita María
%T On the classification of 3-bridge links.
%D 2012
%@ 0034-7426
%U https://hdl.handle.net/20.500.14352/43833
%X Using a new way to represent links, that we call a buttery representation, we assign to each 3-bridge link diagram a sequence of six integers,collected as a triple (p=n; q=m; s=l), such that p  q  s  2, 0 < n  p,0 < m  q and 0 < l  s. For each 3-bridge link there exists an innite number of 3-bridge diagrams, so we dene an order in the set (p=n; q=m; s=l) and assign to each 3-bridge link L the minimum among all the triples that correspond to a 3-butter y of L, and call it the butter y presentation of L. This presentation extends, in a natural way, the well known Schubert classication of 2-bridge links.We obtain necessary and sucient conditions for a triple (p=n; q=m; s=l) to correspond to a 3-butter y and so, to a 3-bridge link diagram. Given a triple (p=n; q=m; s=l) we give an algorithm to draw a canonical 3-bridge diagram ofthe associated link. We present formulas for a 3-buttery of the mirror image of a link, for the connected sum of two rational knots and for some important families of 3-bridge links. We present the open question: When do the triples (p=n; q=m; s=l) and (p 0 =n0 ; q0 =m0 ; s0 =l0) represent the same 3-bridge link?
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