Publication:
Khovanov homology for (3, k)-torus knots
Khovanov homology for (3, k)-torus knots
dc.contributor.advisor | Ortiz-Navarro, Juan A. | |
dc.contributor.author | Rocha-Fontalvo, Yolima A. | |
dc.contributor.college | College of Arts and Sciences - Sciences | en_US |
dc.contributor.committee | Dziobiak, Stan | |
dc.contributor.committee | Romero, Juan | |
dc.contributor.department | Department of Mathematics | en_US |
dc.contributor.representative | Coutin, Sandra | |
dc.date.accessioned | 2017-08-15T18:42:56Z | |
dc.date.available | 2017-08-15T18:42:56Z | |
dc.date.issued | 2016 | |
dc.description.abstract | This thesis studies the construction of Khovanov homology for (3, k)-torus knots by using combinatorial topology and skein theory, identifying common characteristics of Khovanov Bracket for (3, k)-torus knots. The r-th homology, Hr , of the complex C is calculated explicitly for r = 0, 1, 2k − 1 and 2k, it allows to obtain some exponents of the variables q and t in the graded Poincaré polynomial of the complex C, which is called the Khovanov bracket. | |
dc.description.abstract | En esta tesis se analiza la construcción de la homología de Khovanov para nudos toroidales (3, k) mediante el uso de la topología combinatorial y teoría de skein, identificando características comunes del bracket de Khovanov para nudos toroidales (3, k). La r-ésima homología, Hr , del complejo C se calcula de forma explícita para r = 0, 1, 2k − 1 y 2k, lo que permite obtener algunos exponentes de las variables q y t en el polinomio de Poincaré del complejo C, el cual es llamado Khovanov bracket. | |
dc.description.graduationSemester | Summer | en_US |
dc.description.graduationYear | 2016 | en_US |
dc.identifier.uri | https://hdl.handle.net/20.500.11801/34 | |
dc.language.iso | en | en_US |
dc.rights.holder | (c) 2016 Yolima Auxiliadora Rocha Fontalvo | en_US |
dc.rights.license | All rights reserved | en_US |
dc.subject | torus | en_US |
dc.subject.lcsh | Torus (Geometry) | en_US |
dc.subject.lcsh | Combinatorial topology | en_US |
dc.subject.lcsh | Knot theory | en_US |
dc.title | Khovanov homology for (3, k)-torus knots | en_US |
dc.title.alternative | Homología de Khovanov para nudos toroidales (3, k) | 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 |