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dc.contributor.advisorOrtiz-Navarro, Juan A.
dc.contributor.authorMontoya-Vega, Gabriel
dc.date.accessioned2018-10-10T19:36:25Z
dc.date.available2018-10-10T19:36:25Z
dc.date.issued2017
dc.identifier.urihttps://hdl.handle.net/20.500.11801/1020
dc.description.abstractThe large quantity of almost alternating knots gives rise to an important category in knot classification. We thus establish a result, previously given for the span of the bracket polynomial for almost alternating knots, in terms of the Jones polynomial. The Khovanov complex of a given knot K is generated by considering a planar projection of the knot with 2ⁿ states, each of which consists of a collection of simple closed curves in the plane. Following results in leading papers, we find which specific knots differ from others satisfying an equation and we present an alternative proof of a theorem related to the span of the Jones polynomial of an almost alternating knot; finally, keeping up our idea of finding invariants, we study their Khovanov homology.en_US
dc.description.abstractLa gran cantidad de nudos casi alternantes da lugar a una importante categoría en la clasificación de los nudos. Así, se establece un resultado previamente dado para la diferencia entre las potencias mayor y menor que ocurren en el polinomio bracket de nudos casi alternantes, en términos del polinomio de Jones. El complejo de Khovanov para un nudo K se genera al considerar una proyeccion planar del nudo con 2ⁿ estados, cada uno de los cuales consiste en una colección de curvas cerradas simples en el plano. Siguiendo resultados de artículos destacados, encontramos los nudos que difieren de otros al no satisfacer cierta ecuación y presentamos una prueba alternativa para un teorema relativo a la diferencia entre las potencias mayor y menor que ocurren en el polinomio de Jones para nudos casi alternantes. Por último y manteniendo nuestra idea de encontrar invariantes, estudiamos la homología de Khovanov para esos nudos.en_US
dc.language.isoenen_US
dc.subjectJones Polynomialen_US
dc.subjectKhovanov homologyen_US
dc.subject.lcshKnot polynomialsen_US
dc.titleKhovanov homology for almost alternating knotsen_US
dc.typeThesisen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2017 Gabriel Montoya Vegaen_US
dc.contributor.committeeCastellini, Gabriele
dc.contributor.committeeRomero-Oliveras, Juan
dc.contributor.representativeMorell-Cruz, Luis
thesis.degree.levelM.S.en_US
thesis.degree.disciplinePure Mathematicsen_US
dc.contributor.collegeCollege of Arts and Sciences - Sciencesen_US
dc.contributor.departmentDepartment of Mathematicsen_US
dc.description.graduationYear2017en_US


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    Items included under this collection are theses, dissertations, and project reports submitted as a requirement for completing a graduate degree at UPR-Mayagüez.

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