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Creators/Authors contains: "Montoya-Vega, Gabriel"

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  1. ; (, Journal of Knot Theory and Its Ramifications)
    Gram determinants earned traction among knot theorists after Witten’s presumption about the existence of a 3-manifold invariant connected to the Jones polynomial. Triggered by the creation of such an invariant by Reshetikhin and Turaev, several mathematicians have explored this line of research ever since. Gram determinants came into play by Lickorish’s skein theoretic approach to the invariant. The construction of different bilinear forms is possible through changes in the ambient surface of the Kauffman bracket skein module. Hence, different types of Gram determinants have arisen in knot theory throughout the years; some of these determinants are discussed here. In this paper, we introduce a new version of such a determinant from the Möbius band and prove some important results about its structure. In particular, we explore its connection to the annulus case and factors of its closed formula. 
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  2. (, Revista Integración)
    La teoría matemática de nudos estudia las incrustaciones de círculos en el espacio R^3. La introducción de teorías de homología produce estructuras matemáticas complejas generando nuevas oportunidades de investigación. En este artículo brindamos una primera mirada a la homología de Khovanov, a la sucesión larga de Khovanov y se presenta un resumen de los orígenes históricos de la teoría. Además usamos esta sucesión para calcular la homología de los nudos toroidales T(2, n). Uno de los objetivos principales de esta publicación es fomentar el estudio de la teoría de nudos y la homología de Khovanov en Colombia y Latinoamérica en general. 
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