Harmonic analysis and the topology of spheres
The goal of this undergraduate thesis is to study the harmonic analysis in homogeneous spaces, based on the theory of representations of compact Lie groups, and how we can use this theory to find topological invariants of those spaces. Specifically, it deals with the case of spheres S^n, which can b...
- Autores:
-
Gómez Cobos, David Santiago
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2019
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/39278
- Acceso en línea:
- http://hdl.handle.net/1992/39278
- Palabra clave:
- Análisis armónico
Grupos de Lie
Espacios homogéneos
Invariantes
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cardona Guio, Alexandervirtual::2629-1Gómez Cobos, David Santiago2fd28102-704c-4c9f-a224-9cfe8280cae8400Malakhaltsev, Mikhail A.2020-06-10T16:08:49Z2020-06-10T16:08:49Z2019http://hdl.handle.net/1992/39278u821182.pdfinstname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/The goal of this undergraduate thesis is to study the harmonic analysis in homogeneous spaces, based on the theory of representations of compact Lie groups, and how we can use this theory to find topological invariants of those spaces. Specifically, it deals with the case of spheres S^n, which can be seen as homogeneous spaces by means of the quotient of special orthogonal groups SO(n + 1) / SO(n), and explicit calculations of its Euler character are presented. The latter with the help of the Hodge decomposition theorem and the index theorem for the Dirac-de Rham operator on the sphere"El objetivo de esta tesis de pregrado es estudiar el análisis armónico en espacios homogéneos, basado en la teoría de representaciones de grupos de Lie compactos, y cómo podemos usar esta teoría para encontrar invariantes topológicos de dichos espacios. Concretamente, se trata el caso de las esferas S^n, las cuales pueden ser vistas como espacios homogéneos por medio del cociente de grupos ortogonales especiales SO(n + 1) / SO(n), y se presentan cálculos explícitos de su característica de Euler. Esto último con la ayuda del teorema de descomposición de Hodge y el teorema de índice para el operador de Dirac-de Rham en la esfera."--Tomado del Formato de Documento de GradoMatemáticoPregrado52 hojasapplication/pdfengUniversidad de los AndesMatemáticasFacultad de CienciasDepartamento de Matemáticasinstname:Universidad de los Andesreponame:Repositorio Institucional SénecaHarmonic analysis and the topology of spheresTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesishttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TPAnálisis armónicoGrupos de LieEspacios homogéneosInvariantesMatemáticasPublicationb65b9b87-c23b-4157-ac5a-55f34b071dc7virtual::2629-1b65b9b87-c23b-4157-ac5a-55f34b071dc7virtual::2629-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000055190virtual::2629-1ORIGINALu821182.pdfapplication/pdf352375https://repositorio.uniandes.edu.co/bitstreams/5e6dee9b-885d-4c06-b1ca-c8fbcbe90b36/download818343c47d38f28093d11fa2da7be773MD51THUMBNAILu821182.pdf.jpgu821182.pdf.jpgIM Thumbnailimage/jpeg6261https://repositorio.uniandes.edu.co/bitstreams/25bb1207-cd64-408f-96ff-6535a6bf4aa9/downloada5531185f3e2033fd6012168696df7b3MD55TEXTu821182.pdf.txtu821182.pdf.txtExtracted texttext/plain80492https://repositorio.uniandes.edu.co/bitstreams/5f00e23f-3cbe-4d76-9a2f-4212a409a198/downloada4c6503473dff2143364f8fb77e6d1a7MD541992/39278oai:repositorio.uniandes.edu.co:1992/392782024-03-13 12:14:50.301http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.co |
| dc.title.es_CO.fl_str_mv |
Harmonic analysis and the topology of spheres |
| title |
Harmonic analysis and the topology of spheres |
| spellingShingle |
Harmonic analysis and the topology of spheres Análisis armónico Grupos de Lie Espacios homogéneos Invariantes Matemáticas |
| title_short |
Harmonic analysis and the topology of spheres |
| title_full |
Harmonic analysis and the topology of spheres |
| title_fullStr |
Harmonic analysis and the topology of spheres |
| title_full_unstemmed |
Harmonic analysis and the topology of spheres |
| title_sort |
Harmonic analysis and the topology of spheres |
| dc.creator.fl_str_mv |
Gómez Cobos, David Santiago |
| dc.contributor.advisor.none.fl_str_mv |
Cardona Guio, Alexander |
| dc.contributor.author.none.fl_str_mv |
Gómez Cobos, David Santiago |
| dc.contributor.jury.none.fl_str_mv |
Malakhaltsev, Mikhail A. |
| dc.subject.keyword.es_CO.fl_str_mv |
Análisis armónico Grupos de Lie Espacios homogéneos Invariantes |
| topic |
Análisis armónico Grupos de Lie Espacios homogéneos Invariantes Matemáticas |
| dc.subject.themes.none.fl_str_mv |
Matemáticas |
| description |
The goal of this undergraduate thesis is to study the harmonic analysis in homogeneous spaces, based on the theory of representations of compact Lie groups, and how we can use this theory to find topological invariants of those spaces. Specifically, it deals with the case of spheres S^n, which can be seen as homogeneous spaces by means of the quotient of special orthogonal groups SO(n + 1) / SO(n), and explicit calculations of its Euler character are presented. The latter with the help of the Hodge decomposition theorem and the index theorem for the Dirac-de Rham operator on the sphere |
| publishDate |
2019 |
| dc.date.issued.none.fl_str_mv |
2019 |
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2020-06-10T16:08:49Z |
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2020-06-10T16:08:49Z |
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Trabajo de grado - Pregrado |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/bachelorThesis |
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http://purl.org/coar/resource_type/c_7a1f |
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http://hdl.handle.net/1992/39278 |
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u821182.pdf |
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reponame:Repositorio Institucional Séneca |
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repourl:https://repositorio.uniandes.edu.co/ |
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http://hdl.handle.net/1992/39278 |
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u821182.pdf instname:Universidad de los Andes reponame:Repositorio Institucional Séneca repourl:https://repositorio.uniandes.edu.co/ |
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eng |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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52 hojas |
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Universidad de los Andes |
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Matemáticas |
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Facultad de Ciencias |
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Departamento de Matemáticas |
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