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https://hdl.handle.net/2445/221203
Title: | Introduction to contact topology |
Author: | Velasco Soldevila, Eduard |
Director/Tutor: | Cardona Aguilar, Robert |
Keywords: | Topologia Topologia diferencial Treballs de fi de màster Topology Differential topology Master's thesis |
Issue Date: | 9-Jan-2025 |
Abstract: | 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. |
Note: | Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Any: 2025. Director: Robert Cardona Aguilar |
URI: | https://hdl.handle.net/2445/221203 |
Appears in Collections: | Màster Oficial - Matemàtica Avançada |
Files in This Item:
File | Description | Size | Format | |
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tfm_velasco_soldevila_eduard.pdf | Memòria | 4.43 MB | Adobe PDF | View/Open |
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