Introducción a las descomposiciones de Heegaard y la homología de Heegaard-Floer.

dc.contributor.advisorToro Villegas, Margarita María
dc.contributor.authorZapata Rendón, Sebastian
dc.date.accessioned2021-09-29T20:44:45Z
dc.date.available2021-09-29T20:44:45Z
dc.date.issued2021
dc.descriptionilustracionesspa
dc.description.abstractSe estudia a fondo la construcción de las descomposiciones de Heegaard, haciendo énfasis en el por qué es una herramienta central en el estudio de las 3-variedades. Para esto, analizamos las 3-variedades desde las categorías topológica, suave y triángulable, en donde siempre podemos derivar el concepto de descomposición de Heegaard como algo arraigado a la 3-variedad misma. Luego de esto se explora uno de los invariantes de 3-variedades más recientes, la homología de Heegaard-Floer, centrándonos en la aparición de las descomposiciones de Heegaard en su construcción, sirviendo así como eje motivador para futuros proyectos. (Texto tomado de la fuente)spa
dc.description.abstractThe construction of Heegaard decompositions is studied in depth, emphasizing why it is a central tool in the study of 3-manifolds. For this, we analyze the 3-manifolds from the topological, smooth and triangular categories, where we can always derive the Heegaard decomposition concept as something rooted in the 3-manifold itself. After this, one of the most recent 3-manifold invariants is explored, the Heegaard-Floer homology, focusing on the appearance of Heegaard decompositions in its construction, and thus serving as a motivating axis for future projects.eng
dc.description.degreelevelMaestríaspa
dc.description.degreenameMagíster en Ciencias - Matemáticasspa
dc.format.extent83 páginasspa
dc.format.mimetypeapplication/pdfspa
dc.identifier.instnameUniversidad Nacional de Colombiaspa
dc.identifier.reponameRepositorio Institucional Universidad Nacional de Colombiaspa
dc.identifier.repourlhttps://repositorio.unal.edu.co/spa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/80340
dc.language.isospaspa
dc.publisherUniversidad Nacional de Colombiaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Medellínspa
dc.publisher.departmentEscuela de matemáticasspa
dc.publisher.facultyFacultad de Cienciasspa
dc.publisher.placeMedellín, Colombiaspa
dc.publisher.programMedellín - Ciencias - Maestría en Ciencias - Matemáticasspa
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dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseReconocimiento 4.0 Internacionalspa
dc.rights.urihttp://creativecommons.org/licenses/by-nc/4.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.lembVariedades (Algebra universal)spa
dc.subject.lembVarieties (Universal algebra)eng
dc.subject.proposalHeegaard-Floerspa
dc.subject.proposalHeegaard-Floereng
dc.subject.proposalDescomposiciones de Heegaardspa
dc.subject.proposalHeegaard splittingeng
dc.subject.proposal3 Variedadesspa
dc.subject.proposal3 Manifoldseng
dc.subject.proposalCuerpos de asasspa
dc.subject.proposalHandlebodyeng
dc.subject.proposalComplex curveeng
dc.subject.proposalComplejo de curvasspa
dc.subject.proposalEspacios lenticularesspa
dc.subject.proposalLens spaceseng
dc.titleIntroducción a las descomposiciones de Heegaard y la homología de Heegaard-Floer.spa
dc.title.translatedIntroduction to Heegaard splittings and Heegaard-Floer Homology.eng
dc.typeTrabajo de grado - Maestríaspa
dc.type.coarhttp://purl.org/coar/resource_type/c_bdccspa
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aaspa
dc.type.contentTextspa
dc.type.driverinfo:eu-repo/semantics/masterThesisspa
dc.type.redcolhttp://purl.org/redcol/resource_type/TMspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
dcterms.audience.professionaldevelopmentInvestigadoresspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

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