<?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>0034-7426</journal-id>
<journal-title><![CDATA[Revista Colombiana de Matemáticas]]></journal-title>
<abbrev-journal-title><![CDATA[Rev.colomb.mat.]]></abbrev-journal-title>
<issn>0034-7426</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0034-74262018000100009</article-id>
<article-id pub-id-type="doi">10.15446/recolma.v1n52.74525</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Stabilization of the Homotopy Groups of the Moduli Spaces of k-Higgs Bundles]]></article-title>
<article-title xml:lang="es"><![CDATA[Estabilización de los Grupos de Homotopía de los Espacios Móduli de los k-Fibrados de Higgs]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Zúñiga-Rojas]]></surname>
<given-names><![CDATA[Ronald A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Costa Rica UCR  ]]></institution>
<addr-line><![CDATA[San José ]]></addr-line>
<country>Costa Rica</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2018</year>
</pub-date>
<volume>52</volume>
<numero>1</numero>
<fpage>9</fpage>
<lpage>31</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0034-74262018000100009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0034-74262018000100009&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0034-74262018000100009&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The work of Hausel proves that the Bia&#322;ynicki-Birula stratification of the moduli space of rank two Higgs bundles coincides with its Shatz stratification. He uses that to estimate some homotopy groups of the moduli spaces of k-Higgs bundles of rank two. Unfortunately, those two stratifications do not coincide in general. Here, the objective is to present a different proof of the stabilization of the homotopy groups of M k (2, d), and generalize it to M k (3, d), the moduli spaces of k-Higgs bundles of degree d, and ranks two and three respectively, over a compact Riemann surface X, using the results from the works of Hausel and Thaddeus, among other tools.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: El trabajo de Hausel prueba que la estratificación de Bia&#322;ynicki-Birula del espacio moduli de fibrados de Higgs de rango dos coincide con su estratificación de Shatz. Él usa este hecho para calcular algunos grupos de homotopía del espacio moduli de k-fibrados de Higgs de rango dos. Desafortunadamente, estas dos estratificaciones no coinciden en general. Aquí, el objetivo es presentar una prueba diferente de la estabilización de los grupos de homotopía de M k (2, d), y generalizarla a Mk(3, d), los espacios moduli de k-fibrados de Higgs de grado d, y rangos dos y tres respectivamente, sobre una superficie de Riemann compacta X, usando los resultados de los trabajos de Hausel y Thaddeus, entre otras herramientas.]]></p></abstract>
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<kwd lng="en"><![CDATA[Moduli of Higgs Bundles]]></kwd>
<kwd lng="en"><![CDATA[Variations of Hodge Structures]]></kwd>
<kwd lng="en"><![CDATA[Vector Bundles]]></kwd>
<kwd lng="es"><![CDATA[Moduli de Fibrados de Higgs]]></kwd>
<kwd lng="es"><![CDATA[Variaciones de Estructuras de Hodge]]></kwd>
<kwd lng="es"><![CDATA[Fibrados Vectoriales]]></kwd>
</kwd-group>
</article-meta>
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