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http://hdl.handle.net/2445/151137
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DC Field | Value | Language |
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dc.contributor.advisor | Gutiérrez Marín, Javier J. | - |
dc.contributor.author | Prieto de la Cruz, Ángel | - |
dc.date.accessioned | 2020-02-25T08:44:55Z | - |
dc.date.available | 2020-02-25T08:44:55Z | - |
dc.date.issued | 2019-06-20 | - |
dc.identifier.uri | http://hdl.handle.net/2445/151137 | - |
dc.description | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2019, Director: Javier J. Gutiérrez Marín | ca |
dc.description.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. | ca |
dc.format.extent | 56 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | ca |
dc.rights | cc-by-nc-nd (c) Ángel Prieto de la Cruz, 2019 | - |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ | * |
dc.source | Treballs Finals de Grau (TFG) - Matemàtiques | - |
dc.subject.classification | Topologia de baixa dimensió | ca |
dc.subject.classification | Treballs de fi de grau | - |
dc.subject.classification | Varietats topològiques | ca |
dc.subject.classification | Varietats topològiques de dimensió 3 | ca |
dc.subject.other | Low-dimensional topology | en |
dc.subject.other | Bachelor's theses | - |
dc.subject.other | Topological manifolds | en |
dc.subject.other | Three-manifolds (Topology) | en |
dc.title | The geometrisation conjecture of 3-manifolds | ca |
dc.type | info:eu-repo/semantics/bachelorThesis | ca |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | ca |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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151137.pdf | Memòria | 694.15 kB | Adobe PDF | View/Open |
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