<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2023000200103</article-id>
<article-id pub-id-type="doi">10.18273/revint.v41n2-2023003</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Una mirada inicial a la teoría de nudos y a la homología de Khovanov]]></article-title>
<article-title xml:lang="en"><![CDATA[A first look at knot theory and Khovanov homology]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Montoya-Vega]]></surname>
<given-names><![CDATA[Gabriel]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Rico-Río Piedras  ]]></institution>
<addr-line><![CDATA[San Juan ]]></addr-line>
<country>Puerto Rico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2023</year>
</pub-date>
<volume>41</volume>
<numero>2</numero>
<fpage>103</fpage>
<lpage>123</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2023000200103&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2023000200103&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2023000200103&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. La teoría matemática de nudos estudia los encajamientos de círculos en el espacio &#8477;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 dicha 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.  MSC2010:  01A05, 57K10, 57K14, 57K18.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. The mathematical theory of knots studies the embeddings of circles into the space &#8477;3. The introduction of homology theories results in complex mathematical structures that generate new research opportunities. In this article, we offer a first look into Khovanov homology, the long exact sequence of Khovanov homology, and we present a summary of the historical origins of the theory. Moreover, we use this sequence to calculate the homology of torus knots T (2, n). One of the the main objectives in publishing this article is to popularize knot theory and Khovanov homology in Colombia and Latin-America in general.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Nudos y enlaces]]></kwd>
<kwd lng="es"><![CDATA[polinomio bracket]]></kwd>
<kwd lng="es"><![CDATA[homología de Khovanov]]></kwd>
<kwd lng="es"><![CDATA[sucesión larga de la homología de Khovanov]]></kwd>
<kwd lng="es"><![CDATA[nudos toroidales]]></kwd>
<kwd lng="en"><![CDATA[Knots and links]]></kwd>
<kwd lng="en"><![CDATA[bracket polynomial]]></kwd>
<kwd lng="en"><![CDATA[Khovanov homology]]></kwd>
<kwd lng="en"><![CDATA[long exact sequence of Khovanov homology]]></kwd>
<kwd lng="en"><![CDATA[torus knots]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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