On the topological proof of the Mumford conjecture

This dissertation is a introductory monograph on the topological viewpoint of Mumford’s conjecture. The first part studies the homotopy theoretical tools of infinite loop spaces, the Group Completion Theorem and the plus construction. The second part is a survey about the development of the problem...

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Autores:
Mejía Gómez, Tomás
Tipo de recurso:
Fecha de publicación:
2018
Institución:
Universidad Nacional de Colombia
Repositorio:
Universidad Nacional de Colombia
Idioma:
spa
OAI Identifier:
oai:repositorio.unal.edu.co:unal/64092
Acceso en línea:
https://repositorio.unal.edu.co/handle/unal/64092
http://bdigital.unal.edu.co/64851/
Palabra clave:
5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Mumford’s conjecture
Group completion
Plus construction
Madsen-Weiss theorem
Infinite loop spaces
Conjetura de Mumford
Teorema de Madsen-Weiss
Espacios de bucle infinitos
Rights
openAccess
License
Atribución-NoComercial 4.0 Internacional
id UNACIONAL2_b597684321e74eb4dc7f5f8ab78636f3
oai_identifier_str oai:repositorio.unal.edu.co:unal/64092
network_acronym_str UNACIONAL2
network_name_str Universidad Nacional de Colombia
repository_id_str
spelling Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Gómez Guerra, José Manuel (Thesis advisor)e75dd2ca-91aa-42bc-85f3-43a458f57b9e-1Mejía Gómez, Tomás566154d5-4410-4a5c-9c33-6c8f4d78b6183002019-07-02T22:29:52Z2019-07-02T22:29:52Z2018https://repositorio.unal.edu.co/handle/unal/64092http://bdigital.unal.edu.co/64851/This dissertation is a introductory monograph on the topological viewpoint of Mumford’s conjecture. The first part studies the homotopy theoretical tools of infinite loop spaces, the Group Completion Theorem and the plus construction. The second part is a survey about the development of the problem from the original formulation of the conjecture to the Generalized Madsen-Weiss Theorem and its proof.Maestríaapplication/pdfspaUniversidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de MatemáticasEscuela de MatemáticasMejía Gómez, Tomás (2018) On the topological proof of the Mumford conjecture. Maestría thesis, Universidad Nacional de Colombia -Sede Medellín.5 Ciencias naturales y matemáticas / Science51 Matemáticas / MathematicsMumford’s conjectureGroup completionPlus constructionMadsen-Weiss theoremInfinite loop spacesConjetura de MumfordTeorema de Madsen-WeissEspacios de bucle infinitosOn the topological proof of the Mumford conjectureTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMORIGINAL1036948883.2018.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf523809https://repositorio.unal.edu.co/bitstream/unal/64092/1/1036948883.2018.pdf87735220a55aae39cd6ec130e27189b2MD51THUMBNAIL1036948883.2018.pdf.jpg1036948883.2018.pdf.jpgGenerated Thumbnailimage/jpeg4027https://repositorio.unal.edu.co/bitstream/unal/64092/2/1036948883.2018.pdf.jpg654529b48dc5014237838d660a65f3c4MD52unal/64092oai:repositorio.unal.edu.co:unal/640922023-04-25 23:07:48.0Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co
dc.title.spa.fl_str_mv On the topological proof of the Mumford conjecture
title On the topological proof of the Mumford conjecture
spellingShingle On the topological proof of the Mumford conjecture
5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Mumford’s conjecture
Group completion
Plus construction
Madsen-Weiss theorem
Infinite loop spaces
Conjetura de Mumford
Teorema de Madsen-Weiss
Espacios de bucle infinitos
title_short On the topological proof of the Mumford conjecture
title_full On the topological proof of the Mumford conjecture
title_fullStr On the topological proof of the Mumford conjecture
title_full_unstemmed On the topological proof of the Mumford conjecture
title_sort On the topological proof of the Mumford conjecture
dc.creator.fl_str_mv Mejía Gómez, Tomás
dc.contributor.advisor.spa.fl_str_mv Gómez Guerra, José Manuel (Thesis advisor)
dc.contributor.author.spa.fl_str_mv Mejía Gómez, Tomás
dc.subject.ddc.spa.fl_str_mv 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
topic 5 Ciencias naturales y matemáticas / Science
51 Matemáticas / Mathematics
Mumford’s conjecture
Group completion
Plus construction
Madsen-Weiss theorem
Infinite loop spaces
Conjetura de Mumford
Teorema de Madsen-Weiss
Espacios de bucle infinitos
dc.subject.proposal.spa.fl_str_mv Mumford’s conjecture
Group completion
Plus construction
Madsen-Weiss theorem
Infinite loop spaces
Conjetura de Mumford
Teorema de Madsen-Weiss
Espacios de bucle infinitos
description This dissertation is a introductory monograph on the topological viewpoint of Mumford’s conjecture. The first part studies the homotopy theoretical tools of infinite loop spaces, the Group Completion Theorem and the plus construction. The second part is a survey about the development of the problem from the original formulation of the conjecture to the Generalized Madsen-Weiss Theorem and its proof.
publishDate 2018
dc.date.issued.spa.fl_str_mv 2018
dc.date.accessioned.spa.fl_str_mv 2019-07-02T22:29:52Z
dc.date.available.spa.fl_str_mv 2019-07-02T22:29:52Z
dc.type.spa.fl_str_mv Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv Text
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/TM
status_str acceptedVersion
dc.identifier.uri.none.fl_str_mv https://repositorio.unal.edu.co/handle/unal/64092
dc.identifier.eprints.spa.fl_str_mv http://bdigital.unal.edu.co/64851/
url https://repositorio.unal.edu.co/handle/unal/64092
http://bdigital.unal.edu.co/64851/
dc.language.iso.spa.fl_str_mv spa
language spa
dc.relation.ispartof.spa.fl_str_mv Universidad Nacional de Colombia Sede Medellín Facultad de Ciencias Escuela de Matemáticas
Escuela de Matemáticas
dc.relation.references.spa.fl_str_mv Mejía Gómez, Tomás (2018) On the topological proof of the Mumford conjecture. Maestría thesis, Universidad Nacional de Colombia -Sede Medellín.
dc.rights.spa.fl_str_mv Derechos reservados - Universidad Nacional de Colombia
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.license.spa.fl_str_mv Atribución-NoComercial 4.0 Internacional
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv Atribución-NoComercial 4.0 Internacional
Derechos reservados - Universidad Nacional de Colombia
http://creativecommons.org/licenses/by-nc/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.mimetype.spa.fl_str_mv application/pdf
institution Universidad Nacional de Colombia
bitstream.url.fl_str_mv https://repositorio.unal.edu.co/bitstream/unal/64092/1/1036948883.2018.pdf
https://repositorio.unal.edu.co/bitstream/unal/64092/2/1036948883.2018.pdf.jpg
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bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
repository.name.fl_str_mv Repositorio Institucional Universidad Nacional de Colombia
repository.mail.fl_str_mv repositorio_nal@unal.edu.co
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