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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 thesis
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
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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