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