{"id":33735,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/sobre-los-espacios-de-categoria-dos\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"sobre-los-espacios-de-categoria-dos","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/sobre-los-espacios-de-categoria-dos\/","title":{"rendered":"Sobre los espacios de categoria dos."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Lucia Fernandez Suarez <\/strong><\/h2>\n<p>La l.S. Categor\u00eda de una variedad diferenciable m, o simplemente categor\u00eda, fue introducida en 1934 por lusternik y schnirelmann para acotar inferiormente el n\u00famero de puntos cr\u00edticos de una funci\u00f3n diferenciable f : m &#8212; r. En general, para un espacio topol\u00f3gico a, fox define su categor\u00eda, cata, como el m\u00ednimo natural n tal que a admite un recubrimiento por n + 1 abiertos contr\u00e1ctiles en a. La categor\u00eda es un invariante del tipo de homotop\u00eda dif\u00edcil de calcular directamente a pesar de la existencia de caracterizaciones proporcionadas por whitehead y ganea. Otra manera de calcular cat es mediante aproximaciones, como por ejemplo la categor\u00eda fuerte de un cw-complejo k, catk, introducida en 1960 por ganea.  la relaci\u00f3n entre categor\u00eda y categor\u00eda fuerte es la siguiente:  catk &lt;= catk &lt;= catk + 1 en la primera parte de la tesis nos ocupamos de la primera desigualdad, demostrando que exigiendo a k ciertas condiciones se tiene que catk &lt;= 2 implica catk &lt;= 2.  en la segunda parte de la tesis, consideramos la desigualdad demostrada por takens:  cat(k x n) &lt;= catk + max {catn,1} y resolvemos un problema planteado por ganea, demostrando que la categor\u00eda fuerte de (s3 u e7)x(s3 u e7) localizado en 3 es igual a dos, lo que nos proporciona un ejemplo, sin torsi\u00f3n homol\u00f3gica, donde se tiene la desigualdad estricta.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Sobre los espacios de categoria dos.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Sobre los espacios de categoria dos. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Lucia Fernandez Suarez <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Santiago de compostela<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Daniel Tanr\u00e9<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal:  Masa Vazquez Jos\u00e9 M. <\/li>\n<li>Stephen Halperin (vocal)<\/li>\n<li>Enrique Mac\u00edas Virg\u00f3s (vocal)<\/li>\n<li>Yves Felix (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Lucia Fernandez Suarez La l.S. Categor\u00eda de una variedad diferenciable m, o simplemente categor\u00eda, fue introducida en [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[23405,126,977,585],"tags":[91763,3230,91762,91764,91765,91766],"class_list":["post-33735","post","type-post","status-publish","format-standard","hentry","category-homotopia","category-matematicas","category-santiago-de-compostela","category-topologia","tag-daniel-tanre","tag-enrique-macias-virgos","tag-lucia-fernandez-suarez","tag-masa-vazquez-jose-m","tag-stephen-halperin","tag-yves-felix"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/33735","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=33735"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/33735\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=33735"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=33735"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=33735"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}