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memoria.pdf (772.13 KB)

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Bachelor thesis

Publication date

2018-06-26

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cc-by-nc-nd (c) Josep Esquirol Esteve, 2018
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/125730

Varietats sense accions de $S^{1}$ no trivials

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Ignasi Mundet i Riera

Subject

Grups de Lie, Treballs de fi de grau, Grups de transformacions, Espais topològics, Varietats diferenciables

Subject (English)

Lie groups, Bachelor's theses, Transformation groups, Topological spaces, Differentiable manifolds

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

ESQUIROL ESTEVE, Josep. Varietats sense accions de $S^{1}$ no trivials. [consulted: 16 of August of 2026]. Available at: https://hdl.handle.net/2445/125730

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