{"id":96476,"date":"2009-08-10T00:00:00","date_gmt":"2009-08-10T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/the-geometry-of-the-sopq-higgs-bundles\/"},"modified":"2009-08-10T00:00:00","modified_gmt":"2009-08-10T00:00:00","slug":"the-geometry-of-the-sopq-higgs-bundles","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/geometria\/the-geometry-of-the-sopq-higgs-bundles\/","title":{"rendered":"The geometry of the so(p,q)-higgs bundles."},"content":{"rendered":"<h2>Tesis doctoral de <strong> Marta Aparicio Arroyo <\/strong><\/h2>\n<p>Los fibrados de higgs fueron introducidos por hitchin y son de inter\u00e9s en muchas \u00e1reas de la geometr\u00eda diferencial y algebraica, la topolog\u00eda y la f\u00edsica matem\u00e1tica, como son el estudio de representaciones de una superficie, las teor\u00edas gauge, las geometr\u00edas k\u00ed\u00a4hler e hyperk\u00ed\u00a4hler y los sistemas integrables.  la geometr\u00eda y la topolog\u00eda de los espacios de moduli de g-fibrados de higgs han sido estudiadas para varios grupos de lie complejos reductivos, como gl(n,c), sl(n,c), so(n,c) y sp(2n,c), y para algunas de sus formas reales, como u(p,q), sp(2n,r), entre otras. Esta tesis est\u00e1 dedicada al estudio del espacio de moduli de so_0(p,q)-fibrados de higgs, donde so_0(p,q) es la componente conexa de la identidad del grupo de lie so(p,q).  en esta tesis estudiamos las nociones de semiestabilidad, estabilidad y poliestabilidad para so(n,c) y so_0(p,q)-fibrados de higgs aplicando las nociones generales dadas por garc\u00eda-prada, gothen y mundet i riera, y damos nociones de semiestabilidad y estabilidad simplificadas. Tambi\u00e9n estudiamos las condiciones de lisitud en el moduli.  el uso de t\u00e9cnicas de teor\u00eda de morse para el estudio de la topolog\u00eda de los espacios de moduli de fibrados de higgs fue introducido por hitchin. En esta tesis damos importantes pasos en el estudio del n\u00famero de componentes conexas del espacio de moduli de so_0(p,q)-fibrados de higgs. Nuestro resultado principal es una completa descripci\u00f3n de los m\u00ednimos lisos de la funci\u00f3n de hitchin en dicho espacio de moduli. Tambi\u00e9n construimos la componente de hitchin en los casos split so(n,n) y so(n,n+1). Finalmente resolvemos el problema del c\u00f3mputo de componentes conexas en el caso so_0(1,n) con n impar.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>The geometry of the so(p,q)-higgs bundles.<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 The geometry of the so(p,q)-higgs bundles. <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Marta Aparicio Arroyo <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Salamanca<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/10\/2009<\/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 Hernandez Ruiperez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: vicente Mu\u00f1oz velazquez <\/li>\n<li>Carlos armindo Arango florentino (vocal)<\/li>\n<li>Luis \u00e1lvarez c\u00f3nsul (vocal)<\/li>\n<li>tomas Luis Gomez de  quiroga (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Marta Aparicio Arroyo Los fibrados de higgs fueron introducidos por hitchin y son de inter\u00e9s en muchas [&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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