{"id":78921,"date":"2006-03-03T00:00:00","date_gmt":"2006-03-03T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/homotopa%c2%ada-racional-del-espacio-de-funciones\/"},"modified":"2006-03-03T00:00:00","modified_gmt":"2006-03-03T00:00:00","slug":"homotopa%c2%ada-racional-del-espacio-de-funciones","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/homotopa%c2%ada-racional-del-espacio-de-funciones\/","title":{"rendered":"Homotop\u00edaracional del espacio de funciones"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Urtzi Buijs Mart\u00edn <\/strong><\/h2>\n<p>El objetivo de la presente tesis es comprender el comportamiento racional de ciertas construcciones relacionadas con los espacios de funciones libres y basadas.  la herramienta que constituye el punto de partida de este trabajo es el modelo para el espacio de funciones desarrollado por beown y szczarba haciendo uso del funtor de realizaci\u00f3n de bousfield-gugenheim. A partir de aqu\u00ed se desarrollan modelos para las aplicaciones evaluaci\u00f3n, la evaluaci\u00f3n en el punto base, la aplicaci\u00f3n inducida entre dos espacios de funciones por otra, y la inclusi\u00f3n de un componente en el espacio total, esta \u00faltima partiendo restringir todas las anteriores a un componente particular.  una vez desarrolladas estas herramientas algebraicas se estudian los grupos de homotop\u00eda racional de las componentes del espacio de funciones en t\u00e9rminos de derivaciones relativas a un morfismo, generalizando resultados de lupton y smsith y como aplicaci\u00f3n, m\u00e9todos para trabajar con grupos de gottlieb, entre otros.  a continuaci\u00f3n se da una descripci\u00f3n completa del \u00e1lgebra de lie en homotop\u00eda de las componentes del espacio de funciones, tanto libres como basadas, haciendo uso de las derivaciones relativas, obteniendo como corolario un isomorfismo entre homotop\u00eda racional de la componente de la constante y el producto tensorial de la cohomolog\u00eda de x y la homotop\u00eda de y, generalizando un resultado conocido de vigu\u00e9 en el que prueba esto mismo en el caso en que la dimensi\u00f3n de x es menor que la conectividad de y de tal forma que el espacio de funciones basado escindan como un producto de espacios de eilenberg mac-lane, racionalmente.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Homotop\u00edaracional del espacio de funciones<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Homotop\u00edaracional del espacio de funciones <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Urtzi Buijs Mart\u00edn <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 M\u00e1laga<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 03\/03\/2006<\/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>Aniceto Murillo Mas<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Francisco G\u00f3mez ruiz <\/li>\n<li>daniel Tanr\u00e9 (vocal)<\/li>\n<li>yves F\u00e9lix (vocal)<\/li>\n<li>barry Jessup (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Urtzi Buijs Mart\u00edn El objetivo de la presente tesis es comprender el comportamiento racional de ciertas construcciones [&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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