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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/221203
Introduction to contact topology
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This 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.
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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Robert Cardona Aguilar
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VELASCO SOLDEVILA, Eduard. Introduction to contact topology. [consulted: 20 of May of 2026]. Available at: https://hdl.handle.net/2445/221203