Augmented bundles and real structures

• Autores: Luis Ángel Calvo Pascual
• Directores de la Tesis: Óscar García Prada (dir. tes.)
• Lectura: En la Universidad Autónoma de Madrid ( España ) en 2018
• Idioma: inglés
• Número de páginas: 168
• Tribunal Calificador de la Tesis: Luis Álvarez Cónsul (presid.), Mario García Fernández (secret.), Ignasi Mundet i Riera (voc.)
• Programa de doctorado: Programa de Doctorado en Matemáticas por la Universidad Autónoma de Madrid
• Materias:
  • Matemáticas
    • Geometría
      • Geometría diferencial
• Enlaces
  • Tesis en acceso abierto en: Biblos-e Archivo
• Resumen

  • This thesis is concerned with the study of some augmented bundles equipped with real structures. More specifically, we study: real Higgs pairs, real G-Higgs bundles and real parabolic G-Higgs bundles, where G is a real form of a connected semisimple group G^C. These bundles generalize the notion of pseudo-real Higgs bundles. We prove that they appear naturally as fixed points of involutions in the moduli space of Higgs pairs, G-Higgs bundles and parabolic G-Higgs bundles, respectively. We also prove a non-abelian Hodge correspondence for real G-Higgs bundles and real parabolic G-Higgs bundles.

    The motivation is given by the study of fixed points in the moduli space of augmented bundles and the fact that these fixed points are branes in the sense of Kapustin-Witten in the theory of Geometry Langlands program. Another future research line will be the Higher Teichmuller theory in the presence of real structures.