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dc.contributor.advisorOrtiz-Navarro, Juan A.
dc.contributor.authorBeltrán-Hoyos, Raúl A.
dc.description.abstractThis thesis provides a characterization of the reduced Burau matrices for braids of the form (σ1σ2 · · · σn−1) d , with gcd(n, d) = 1, n, d ≥ 2, and exposes its relationship with the Alexander polynomial for (n, d)-torus knot by using Markov functions theory. In addition, a similar characterization for a particular case of periodic braids is provided, whose closures is the mirror of a (n, d)-torus knot.
dc.description.abstractEsta tesis provee una caraterizaci´on de las matrices reducidas de Burau para trenzas de la forma (σ1σ2 · · · σn−1) d , con mcd(n, d) = 1, n, d ≥ 2, y expone su relaci´on con el polinomio de Alexander para nudos toroidales, usando la teoria de funciones de Markov. En adici´on, proporcionamos una caracterizaci´on similar para un caso particular de trenzas periodicas cuya clausura es el espejo de un (n, d)-nudo toroidal.
dc.subjectBurau matricesen_US
dc.subjectAlexander polynomialen_US
dc.subject.lcshBraid theoryen_US
dc.subject.lcshKnot polynomialsen_US
dc.subject.lcshAlexander idealsen_US
dc.titleAlexander polynomial for torus knots via Burau matrices for periodic braidsen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2017 Raú Alfonso Beltrán Hoyosen_US
dc.contributor.committeeCastellini, Gabriele
dc.contributor.committeeRomero, Juan
dc.contributor.representativeMorales Caro, Betsy Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Arten_US
dc.contributor.departmentDepartment of Mathematicsen_US

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