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Title: The geometrisation conjecture of 3-manifolds
Author: Prieto de la Cruz, Ángel
Director/Tutor: Gutiérrez Marín, Javier J.
Keywords: Topologia de baixa dimensió
Treballs de fi de grau
Varietats topològiques
Varietats topològiques de dimensió 3
Low-dimensional topology
Bachelor's thesis
Topological manifolds
Three-manifolds (Topology)
Issue Date: 20-Jun-2019
Abstract: [en] This thesis aims to be a first approach to Thurston’s geometrisation conjecture, which states that each 3-manifold decomposes canonically into pieces admitting geometric structures. Starting from the definition of a model geometry, we will see first that the only three model geometries in dimension 2 are the Euclidean, the elliptic and the hyperbolic. Then we will show how Thurston’s theorem asserts that there are a total of eight model geometries in dimension 3, and we will classify six of them as Seifert spaces. We will finish by explaining the geometrisation conjecture through a historical perspective, from the first results on sphere and torus decompositions to Perelman’s proof. We will also sketch a proof of the Poincaré conjecture as an immediate corollary.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Javier J. Gutiérrez Marín
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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