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dc.contributor.advisorOrtiz-Navarro, Juan A.
dc.contributor.authorRocha-Fontalvo, Yolima A.
dc.description.abstractThis 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.abstractEn 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.subject.lcshTorus (Geometry)en_US
dc.subject.lcshCombinatorial topologyen_US
dc.subject.lcshKnot theoryen_US
dc.titleKhovanov homology for (3, k)-torus knotsen_US
dc.title.alternativeHomología de Khovanov para nudos toroidales (3, k)en_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2016 Yolima Auxiliadora Rocha Fontalvoen_US
dc.contributor.committeeDziobiak, Stan
dc.contributor.committeeRomero, Juan
dc.contributor.representativeCoutin, Sandra Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US

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