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Geometry of Contact Toric Manifolds in 3D
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
2016 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

In this project we present some applications of symplectic and contact geometry on 3-manifolds. In the first section we introduce the notion of symplectic manifolds and various geometrical objects associated with them, such as the moment map and the Delzant polytope. We also investigate symplectic cuts which are used to create new manifolds from given symplectic manifolds. In the second section we review all the basic definitions that arise from contact geometry such as the contact structure, the contact form and the Reeb vector. Several examples are also used in order to clarify these definitions. In the final section we apply the aforementioned notions to the specific case of Lens spaces, which are 3-manifolds. We also propose a possible application on 5-manifolds which would further expand what was discussed here. 

Place, publisher, year, edition, pages
2016. , 41 p.
Keyword [en]
Symplectic Geometry, Contact Geometry, Lens spaces
National Category
Natural Sciences Physical Sciences
URN: urn:nbn:se:uu:diva-296221OAI: oai:DiVA.org:uu-296221DiVA: diva2:936815
Educational program
Master Programme in Physics
Available from: 2016-06-17 Created: 2016-06-14 Last updated: 2016-06-17Bibliographically approved

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