Orbifolds and geometric structures

In this thesis we study geometric structures on orbifolds. Our main interest lies in the relationship between such structures in orbifolds and corresponding geometric structures of associated manifolds. One instance of this is the symplectic resolution of orbifold singularities in which we associate...

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Detalles Bibliográficos
Autor: Rojo Carulli, Juan Ángel
Tipo de recurso: tesis doctoral
Fecha de publicación:2019
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/17366
Acceso en línea:https://hdl.handle.net/20.500.14352/17366
Access Level:acceso abierto
Palabra clave:515.1
Orbifold
Symplectic Geometry
Sasakian Geometry
Geometría Simpléctica
Geometría Sasakiana
Matemáticas (Matemáticas)
Topología
12 Matemáticas
1210 Topología
Descripción
Sumario:In this thesis we study geometric structures on orbifolds. Our main interest lies in the relationship between such structures in orbifolds and corresponding geometric structures of associated manifolds. One instance of this is the symplectic resolution of orbifold singularities in which we associate a symplectic manifold (the resolution) to a symplectic orbifold. Resolution of symplectic orbifolds is a natural extension to the symplectic category of the classical problem of resolution of singularities in algebraic geometry. Apart from the intrinsic interest of the problem of resolution of singularities in symplectic geometry, resolution of symplectic orbifolds also gives a powerful method to construct symplectic manifolds starting from symplectic orbifolds. With this ideain mind, we develop a method to resolve a certain type of symplectic orbifolds, which we call homegenous isotropy orbifolds. These do not cover orbifolds in full generality, but they suce to construct interesting manifolds...