Lagrangian submanifolds under special conditions of degeneracy of symplectic structures
ilustraciones, diagramas
- Autores:
-
Orozco Macana, Iván Andrés
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84302
- Palabra clave:
- 510 - Matemáticas::516 - Geometría
Geometría
Topología
Geometry
Topology
Symplectic geometry
Lagrangian submanifold
Folded symplectic manifolds
b-symplectic manifolds
- Rights
- openAccess
- License
- Reconocimiento 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| dc.title.translated.spa.fl_str_mv |
Subvariedades Lagrangianas bajo condiciones especiales de degeneración de estructuras simplécticas |
| title |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| spellingShingle |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures 510 - Matemáticas::516 - Geometría Geometría Topología Geometry Topology Symplectic geometry Lagrangian submanifold Folded symplectic manifolds b-symplectic manifolds |
| title_short |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| title_full |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| title_fullStr |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| title_full_unstemmed |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| title_sort |
Lagrangian submanifolds under special conditions of degeneracy of symplectic structures |
| dc.creator.fl_str_mv |
Orozco Macana, Iván Andrés |
| dc.contributor.advisor.none.fl_str_mv |
Martínez Alba, Nicolas |
| dc.contributor.author.none.fl_str_mv |
Orozco Macana, Iván Andrés |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::516 - Geometría |
| topic |
510 - Matemáticas::516 - Geometría Geometría Topología Geometry Topology Symplectic geometry Lagrangian submanifold Folded symplectic manifolds b-symplectic manifolds |
| dc.subject.lemb.spa.fl_str_mv |
Geometría Topología |
| dc.subject.lemb.eng.fl_str_mv |
Geometry Topology |
| dc.subject.proposal.eng.fl_str_mv |
Symplectic geometry Lagrangian submanifold Folded symplectic manifolds b-symplectic manifolds |
| description |
ilustraciones, diagramas |
| publishDate |
2023 |
| dc.date.accessioned.none.fl_str_mv |
2023-07-27T15:03:41Z |
| dc.date.available.none.fl_str_mv |
2023-07-27T15:03:41Z |
| dc.date.issued.none.fl_str_mv |
2023-01 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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https://repositorio.unal.edu.co/handle/unal/84302 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/84302 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
| dc.language.iso.spa.fl_str_mv |
eng |
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eng |
| dc.relation.references.spa.fl_str_mv |
Audin, M., Lafontaine, J., Eds.,. Holomorphic Curves in Symplectic Geometry. Progress in Mathematics 117,birkh¨auser verlag, Basel, 1994. Cannas da Silva, Ana. Introduction to symplectic and Hamiltonian geometry. Publica¸c˜oes Matem´aticas do IMPA. Rio de Janeiro: Instituto Nacional de Matem´atica Pura e Aplicada (IMPA), 2003. Cannas da Silva, Ana. Lectures on symplectic geometry. Lecture Notes in Mathematics 1764, Springer-Verlag, Berlin, (2001). Cannas da Silva, Ana; Guillemin, Victor; Woodward, Christopher. On the unfolding of folded symplectic structures. Math. Res. Lett. 7, No. 1, 35-53, (2000). Cavalcanti, Gil R.; Klaasse, Ralph L. Fibrations and logsymplectic structures. arXiv 1606.00156. Geudens, Stephane; Zambon, Marco. Coisotropic submanifolds in b-symplectic geometry. Can. J. Math. 73, No. 3, 737-768 (2021). Geudens, Stephane; Zambon, Marco. Deformations of Lagrangian submanifolds in log-symplectic manifolds. Adv. Math. 397, Article ID 108202, 85 p. (2022). Guillemin, Victor; Miranda, Eva; Pires, Ana Rita. Symplectic and Poisson geometry on b-manifolds. arXiv 1206.2020v1. Guillemin, Victor; Miranda, Eva; Pires, Ana Rita; Scott, Geoffrey. Toric actions on b-symplectic manifolds. arXiv 1309.1897. Hockensmith, Daniel. A classification of toric, folded-symplectic manifolds. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate College of the University of Illinois at Urbana-Champaign, 2015 Lee, John M. Introduction to smooth manifolds. 2nd revised ed., Graduate Texts in Mathematics 218. New York, NY: Springer, (2013). Marsden, Jerrold E.; Ratiu, Tudor S. Introduction to mechanics and symmetry. A basic exposition of classical mechanical systems. 2nd ed. (English). Texts in Applied Mathematics. 17. New York, NY: Springer. xviii, 582 p. (1999). Meinrenken, Eckhard. SYMPLECTIC GEOMETRY. Lecture Notes, University of Toronto. Available in https://www.math.toronto. edu/mein/teaching/LectureNotes/sympl.pdf Pires, Ana Rita. Origami manifolds. Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June 2010. |
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iv, 43 páginas |
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application/pdf |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Facultad de Ciencias |
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Bogotá,Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Martínez Alba, Nicolas76cf2aaebf3f813a49484f6f39a44543Orozco Macana, Iván Andrés0b0150e9d1e9abf9c11272c0b09963032023-07-27T15:03:41Z2023-07-27T15:03:41Z2023-01https://repositorio.unal.edu.co/handle/unal/84302Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasEl objetivo de este proyecto es estudiar una versión de las subvariedades lagrangianas en estructuras folded-simplecticas y b-simplecticas. Empezaremos estudiando cómo podemos dar una definición de subvariedades isotrópicas, coisotrópicas y Lagrangianas en estas estructuras que sea consistente con la definición de la caso simpléctico, después de eso, a partir de una variedad, construiremos ejemplos canónicos de una subvariedad Lagrangiana en el caso folded-simpléctico y b-simpléctico. Finalmente, haremos una versión del teorema de la vecindad Lagrangiana en estas estructuras. (Texto tomado de la fuente)The aim of this project is to study a version of Lagrangian submanifolds in folded-symplectic and b-symplectic structures. We will start by studying how we can give a definition of isotropic, coisotropic an then Lagrangian submanifold in these structures that is consistent with the definition for the symplectic case, after that, we will considerate certain examples to construct, from a manifold, a canonical examples of a Lagrangian submanifold in a folded-symplectic and b-symplectic manifolds. Finally, we will study a version of Lagrangian neighborhood Theorem applied to folded-symplectic and b-symplectic manifold using the version of Lagrangian submanifolds studied above.MaestríaMagíster en Ciencias - MatemáticasGeometría simplécticaiv, 43 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá,ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::516 - GeometríaGeometríaTopologíaGeometryTopologySymplectic geometryLagrangian submanifoldFolded symplectic manifoldsb-symplectic manifoldsLagrangian submanifolds under special conditions of degeneracy of symplectic structuresSubvariedades Lagrangianas bajo condiciones especiales de degeneración de estructuras simplécticasTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMAudin, M., Lafontaine, J., Eds.,. Holomorphic Curves in Symplectic Geometry. Progress in Mathematics 117,birkh¨auser verlag, Basel, 1994.Cannas da Silva, Ana. Introduction to symplectic and Hamiltonian geometry. Publica¸c˜oes Matem´aticas do IMPA. Rio de Janeiro: Instituto Nacional de Matem´atica Pura e Aplicada (IMPA), 2003.Cannas da Silva, Ana. Lectures on symplectic geometry. Lecture Notes in Mathematics 1764, Springer-Verlag, Berlin, (2001).Cannas da Silva, Ana; Guillemin, Victor; Woodward, Christopher. On the unfolding of folded symplectic structures. Math. Res. Lett. 7, No. 1, 35-53, (2000).Cavalcanti, Gil R.; Klaasse, Ralph L. Fibrations and logsymplectic structures. arXiv 1606.00156.Geudens, Stephane; Zambon, Marco. Coisotropic submanifolds in b-symplectic geometry. Can. J. Math. 73, No. 3, 737-768 (2021).Geudens, Stephane; Zambon, Marco. Deformations of Lagrangian submanifolds in log-symplectic manifolds. Adv. Math. 397, Article ID 108202, 85 p. (2022).Guillemin, Victor; Miranda, Eva; Pires, Ana Rita. Symplectic and Poisson geometry on b-manifolds. arXiv 1206.2020v1.Guillemin, Victor; Miranda, Eva; Pires, Ana Rita; Scott, Geoffrey. Toric actions on b-symplectic manifolds. arXiv 1309.1897.Hockensmith, Daniel. A classification of toric, folded-symplectic manifolds. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics in the Graduate College of the University of Illinois at Urbana-Champaign, 2015Lee, John M. Introduction to smooth manifolds. 2nd revised ed., Graduate Texts in Mathematics 218. New York, NY: Springer, (2013).Marsden, Jerrold E.; Ratiu, Tudor S. Introduction to mechanics and symmetry. A basic exposition of classical mechanical systems. 2nd ed. (English). Texts in Applied Mathematics. 17. New York, NY: Springer. xviii, 582 p. (1999).Meinrenken, Eckhard. SYMPLECTIC GEOMETRY. Lecture Notes, University of Toronto. Available in https://www.math.toronto. edu/mein/teaching/LectureNotes/sympl.pdfPires, Ana Rita. Origami manifolds. Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy, June 2010.EstudiantesInvestigadoresMaestrosORIGINALLagrangian Submanifolds.pdfLagrangian Submanifolds.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf431707https://repositorio.unal.edu.co/bitstream/unal/84302/4/Lagrangian%20Submanifolds.pdf41d238d097e43fe6937573c32973cc6cMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/84302/3/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD53THUMBNAILLagrangian Submanifolds.pdf.jpgLagrangian Submanifolds.pdf.jpgGenerated Thumbnailimage/jpeg4204https://repositorio.unal.edu.co/bitstream/unal/84302/5/Lagrangian%20Submanifolds.pdf.jpga7d082fc4b79e16cfd2111945ad11286MD55unal/84302oai:repositorio.unal.edu.co:unal/843022024-08-14 23:42:41.207Repositorio Institucional Universidad Nacional de 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