Mundet i Riera, IgnasiFerreras Alegre, Jon2023-05-302023-05-302023-01-24https://hdl.handle.net/2445/198640Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Ignasi Mundet i Riera[en] Sard’s theorem is a basic result of Differential Topology which is assumed in many texts of this branch of mathematics. In this work we prove it in detail and we study one of its multiple applications: finding the homotopy type of differentiable manifolds through Morse theory, proving along the way that said theory can be applied to every differentiable manifold.50 p.application/pdfcatcc-by-nc-nd (c) Jon Ferreras Alegre, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Varietats topològiquesTreballs de fi de grauTopologia algebraicaTopologia diferencialTeoria del punt crític (Anàlisi matemàtica)Topological manifoldsBachelor's thesesAlgebraic topologyDifferential topologyCritical point theory (Mathematical analysis)info:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess