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http://hdl.handle.net/2445/125730
Title: | Varietats sense accions de $S^{1}$ no trivials |
Author: | Esquirol Esteve, Josep |
Director/Tutor: | Mundet i Riera, Ignasi |
Keywords: | Grups de Lie Treballs de fi de grau Grups de transformacions Espais topològics Varietats diferenciables Lie groups Bachelor's theses Transformation groups Topological spaces Differentiable manifolds |
Issue Date: | 26-Jun-2018 |
Abstract: | [en] The goal of this work is to prove a non existence theorem of non-trivial $S^{1}$ actions on a certain kind of smooth manifolds. More specifically, let $T$ be the $n$-dimensional torus and $M$ a smooth conected, closed (i.e. compact and without bondary) and orientable manifold of dimension $n$ such that $\chi(T \# M) \neq 0$. Then there are no non-trivial $S^{1}$ actions on $T \neq M$. Before proving this statement, some smooth manifold and Lie group theory will be developed: the proof of the Sard and the Poincaré-Hopf theorems stand out in this part. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Ignasi Mundet i Riera |
URI: | http://hdl.handle.net/2445/125730 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 772.13 kB | Adobe PDF | View/Open |
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