{"id":25234,"date":"2003-09-09T00:00:00","date_gmt":"2003-09-09T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/un-acercamiento-algebraico-a-la-teoria-de-torres-de-postnikov\/"},"modified":"2003-09-09T00:00:00","modified_gmt":"2003-09-09T00:00:00","slug":"un-acercamiento-algebraico-a-la-teoria-de-torres-de-postnikov","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/un-acercamiento-algebraico-a-la-teoria-de-torres-de-postnikov\/","title":{"rendered":"Un acercamiento algebraico a la teor\u00eda de torres de postnikov"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Miguel \u00e1ngel Garc\u00eda Mu\u00f1oz <\/strong><\/h2>\n<p>La torre de postnikov de un espacio es una cadena de fibraciones, las cuales representan los invariantes cohomol\u00f3gicos de un espacio (los \u00abinvariantes de postnikov\u00bb), y cuyas fibras son espacios del tipo k(pi, n). La torre de postnikov de un espacios, todos los objetos xn son espacios y cada invariante de postnikov kn+1 es un elemento en la cohomolog\u00eda singular del espacio xn.  en esta memoria mostramos que es posible usar una aproximaci\u00f3n puramente algebraica para determinar, salvo homotop\u00eda, la torre de postnikov y los invariantes de postnikov de un espacio. Esta aproximaci\u00f3n a la torre de postnikov est\u00e1 basada en la idea de que podemos sustituir cada espacio xn, que es un n-tipo, por un \u00abobjeto algebraico\u00bb, pn(x) que es un modelo para los n-tipos. Entonces en nuestra aproximaci\u00f3n cada piso de la torre de postnikov estar\u00e1 construida en una categor\u00eda diferente, as\u00ed el primer piso se construir\u00e1 en una categor\u00eda (s0) que modela los 0-tipos el primer invariante k1 ser\u00e1 un elemento en una cohomolog\u00eda que debe estar definida en la categor\u00eda s0, el segundo piso estar\u00e1 construido en una categor\u00eda algebraica (s1) que modele los 1-tipos y el segundo invariante de postnikov k2 ser\u00e1 un elemento de una cohomolog\u00eda definida en la categor\u00eda s1, y as\u00ed sucesivamente.  trasladamos esta aproximaci\u00f3n algebraica a la teor\u00eda de torres de postnikov a dos categor\u00edas de modelos de espacios: la categor\u00eda de complejos cruzados y la categor\u00eda de grupoides simpliciales.  presentando diversas aprotaciones de cada uno de los contextos, aportaciones que no solo van dirigidos al estudio de la teor\u00eda de torres de postnikov, sino que por si mismos proporcionan datos relevantes en el estudio de estas categor\u00edas.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Un acercamiento algebraico a la teor\u00eda de torres de postnikov<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Un acercamiento algebraico a la teor\u00eda de torres de postnikov <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Miguel \u00e1ngel Garc\u00eda Mu\u00f1oz <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Granada<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 09\/09\/2003<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Manuel Bullejos Lorenzo<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Antonio Mart\u00ednez  cegarra <\/li>\n<li>Luis Javier Hernandez paricio (vocal)<\/li>\n<li>carles Casacuberta verg\u00e9s (vocal)<\/li>\n<li>Manuel Ladra gonz\u00e1lez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Miguel \u00e1ngel Garc\u00eda Mu\u00f1oz La torre de postnikov de un espacio es una cadena de fibraciones, las [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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