Hilden, Hugh Michael; Montesinos, José María; Tejada Jiménez, Débora María; Toro Villegas, Margarita María (2012)
Abstract:Using a new way to represent links, that we call a butterfly 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 infinite number of 3-bridge diagrams, so we define 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-butterfly of L, and call it the butterfly presentation of L. This presentation extends, in a natural way, the well-known Schubert classification of 2-bridge links. We obtain necessary and sufficient conditions for a triple (p/n, q/m, s/l) to correspond to a 3-butterfly 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-butterfly 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’/n’, q’/m’, s’/l’) represent the same 3-bridge link?
Es proyecto?:no
Autor:Hilden, Hugh Michael
Programa Nal. Colciencias:Programa de ciencias básicas
Insitución cofinanciadora:Departamento Administrativo de Ciencia, Tecnología e Innovación [CO] Colciencias
Institución participante:Universidad Nacional de Colombia, UNAL - Sede Medellín
Tipo de producto resultado de investigación:info:eu-repo/semantics/article
Fecha:2012
Proyecto id:1118-521-28160
Nombre de proyecto principal:Mariposas, enlaces de tres puentes y grupos relacionados
Comunidad vinculada:Comunidad académica de Colombia