Pitsch, WolfgangMundet i Riera, IgnasiCodina Broto, Sergi2024-12-032024-12-032024-06-28https://hdl.handle.net/2445/216886Treballs 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.59 p.application/pdfengcc by-nc-nd (c) Sergi Codina Broto, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Topologia algebraicaEspais fibrats (Matemàtica)Treballs de fi de màsterAlgebraic topologyFiber spaces (Mathematics)Master's thesisinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess