Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Wolfgang Pitsch i Ignasi Mundet i Riera

Detalhes bibliográficos
Autor: Codina Broto, Sergi
Formato: tesis de maestría
Fecha de publicación:2024
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/216886
Acesso em linha:https://hdl.handle.net/2445/216886
Access Level:acceso abierto
Palavra-chave:Topologia algebraica
Espais fibrats (Matemàtica)
Treballs de fi de màster
Algebraic topology
Fiber spaces (Mathematics)
Master's thesis
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spelling Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundlesCodina Broto, SergiTopologia algebraicaEspais fibrats (Matemàtica)Treballs de fi de màsterAlgebraic topologyFiber spaces (Mathematics)Master's thesisTreballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Wolfgang Pitsch i Ignasi Mundet i Riera[en] The aim of this project is to study classifying spaces for $\mathbb{Z} / 2$-equivariant principal $G$-bundles, where $G$ denotes a topological group. In the first chapter, we will study the category of principal $G$-bundles with some important results, including its motivation through the theory of real vector bundles, and the construction of their classifying spaces; reference for this study will be taken from [Die08], [MS74] and [Hus94]. In the second chapter, we introduce the notion of $\Gamma$-equivariant principal $G$ bundles for a topological group $\Gamma$, and follow the work done by Lück and Uribe [LU14] while interested in the specific case $\Gamma=(\mathbb{Z} / 2)$, which allows for simplifications in the proofs of some results which lead to the construction of a model for the classifying space for $\mathbb{Z} / 2$-equivariant principal $G$-bundles, and the subsequent study of the properties of such classifying spaces.Pitsch, WolfgangMundet i Riera, Ignasi2024info:eu-repo/semantics/masterThesisapplication/pdfhttps://hdl.handle.net/2445/216886Màster Oficial - Matemàtica Avançadareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaIngléscc by-nc-nd (c) Sergi Codina Broto, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2168862026-05-27T06:46:51Z
dc.title.none.fl_str_mv Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
title Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
spellingShingle Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
Codina Broto, Sergi
Topologia algebraica
Espais fibrats (Matemàtica)
Treballs de fi de màster
Algebraic topology
Fiber spaces (Mathematics)
Master's thesis
title_short Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
title_full Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
title_fullStr Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
title_full_unstemmed Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
title_sort Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
dc.creator.none.fl_str_mv Codina Broto, Sergi
author Codina Broto, Sergi
author_facet Codina Broto, Sergi
author_role author
dc.contributor.none.fl_str_mv Pitsch, Wolfgang
Mundet i Riera, Ignasi
dc.subject.none.fl_str_mv Topologia algebraica
Espais fibrats (Matemàtica)
Treballs de fi de màster
Algebraic topology
Fiber spaces (Mathematics)
Master's thesis
topic Topologia algebraica
Espais fibrats (Matemàtica)
Treballs de fi de màster
Algebraic topology
Fiber spaces (Mathematics)
Master's thesis
description Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Wolfgang Pitsch i Ignasi Mundet i Riera
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/216886
url https://hdl.handle.net/2445/216886
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv cc by-nc-nd (c) Sergi Codina Broto, 2024
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc by-nc-nd (c) Sergi Codina Broto, 2024
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv Màster Oficial - Matemàtica Avançada
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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