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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/216886
Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles
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[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.
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Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Wolfgang Pitsch i Ignasi Mundet i Riera
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CODINA BROTO, Sergi. Classifying spaces for equivariant $\mathbb{Z} /(2)$-bundles. [consulted: 18 of October of 2026]. Available at: https://hdl.handle.net/2445/216886