Publication:
Alexander polynomial for torus knots via Burau matrices for periodic braids

dc.contributor.advisor Ortiz-Navarro, Juan A.
dc.contributor.author Beltrán-Hoyos, Raúl A.
dc.contributor.college College of Arts and Sciences - Art en_US
dc.contributor.committee Castellini, Gabriele
dc.contributor.committee Romero, Juan
dc.contributor.department Department of Mathematics en_US
dc.contributor.representative Morales Caro, Betsy
dc.date.accessioned 2018-10-10T19:36:20Z
dc.date.available 2018-10-10T19:36:20Z
dc.date.issued 2017
dc.description.abstract . en_US
dc.description.abstract This 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.abstract Esta 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.description.graduationYear 2017 en_US
dc.identifier.uri https://hdl.handle.net/20.500.11801/1019
dc.language.iso en en_US
dc.rights.holder (c) 2017 Raú Alfonso Beltrán Hoyos en_US
dc.rights.license All rights reserved en_US
dc.subject Burau matrices en_US
dc.subject Alexander polynomial en_US
dc.subject.lcsh Braid theory en_US
dc.subject.lcsh Knot polynomials en_US
dc.subject.lcsh Alexander ideals en_US
dc.title Alexander polynomial for torus knots via Burau matrices for periodic braids en_US
dc.type Thesis en_US
dspace.entity.type Publication
thesis.degree.discipline Pure Mathematics en_US
thesis.degree.level M.S. en_US
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