Mundet i Riera, IgnasiEsquirol Esteve, Josep2018-10-302018-10-302018-06-26https://hdl.handle.net/2445/125730Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2018, Director: Ignasi Mundet i Riera[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.51 p.application/pdfcatcc-by-nc-nd (c) Josep Esquirol Esteve, 2018http://creativecommons.org/licenses/by-nc-nd/3.0/es/Grups de LieTreballs de fi de grauGrups de transformacionsEspais topològicsVarietats diferenciablesLie groupsBachelor's thesesTransformation groupsTopological spacesDifferentiable manifoldsinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess