Cardona Aguilar, RobertVelasco Soldevila, Eduard2025-05-262025-05-262025-01-09https://hdl.handle.net/2445/221203Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Robert Cardona AguilarThis master’s thesis provides an introduction to contact topology, with the primary objective of proving Martinet’s Theorem, which asserts that every closed, connected 3-manifold admits a contact structure. The proof heavily relies on the Lickorish-Wallace Theorem, which states that any such 3-manifold can be obtained from $S^{3}$ via a finite sequence of Dehn surgeries. The thesis explores key concepts in contact topology, such as contact structures, Darboux’s Theorem, and Gray stability. A complete proof of the Lickorish-Wallace Theorem is given before focusing on the detailed proof of Martinet’s Theorem, highlighting the ubiquity of contact structures in 3-manifolds.47 p.application/pdfengcc by-nc-nd (c) Eduard Velasco Soldevila, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/TopologiaTopologia diferencialTreballs de fi de màsterTopologyDifferential topologyMaster's thesisinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess