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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| Formato: | tesis doctoral |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/17366 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/17366 |
| Access Level: | acceso abierto |
| Palavra-chave: | 515.1 Orbifold Symplectic Geometry Sasakian Geometry Geometría Simpléctica Geometría Sasakiana Matemáticas (Matemáticas) Topología 12 Matemáticas 1210 Topología |
| Resumo: | 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... |
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