Publication:
Khovanov homology for (3, k)-torus knots

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Authors
Rocha-Fontalvo, Yolima A.
Embargoed Until
Advisor
Ortiz-Navarro, Juan A.
College
College of Arts and Sciences - Sciences
Department
Department of Mathematics
Degree Level
M.S.
Publisher
Date
2016
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.

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.
Keywords
torus
Cite
Rocha-Fontalvo, Y. A. (2016). Khovanov homology for (3, k)-torus knots [Thesis]. Retrieved from https://hdl.handle.net/20.500.11801/34