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oai:docta.ucm.es:20.500.14352/438332023-08-26T07:53:32Zcom_20.500.14352_14col_20.500.14352_15

On the classification of 3-bridge links. Hilden, Hugh Michael Montesinos Amilibia, José María Tejada Jiménez, Débora María Toro Villegas, Margarita María 515.162.8 Links 3-bridge links Bridge presentation Link diagram 3-butterfly Butterfly presentation Geometria algebraica Análisis combinatorio Topología 1201.01 Geometría Algebraica 1202.05 Análisis Combinatorio 1210 Topología Using a new way to represent links, that we call a butter y 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 of the associated link. We present formulas for a 3-butter y 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? Colciencias Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas FALSE pub 2023-06-20T03:32:58Z 2023-06-20T03:32:58Z 2012 journal article https://hdl.handle.net/20.500.14352/43833 0034-7426 eng 1118-521-28160. restricted access application/pdf Soc. Colombiana Mat.