I'm reading some things about algebraic topology, and they mention the classifying space of a group $G$ as $BG$, but they doesn't build one, so I want to ask if someone knows where can I find the way to create one classifying space $BG$ from a given group $G$.
2026-03-25 20:38:19.1774471099
Example of building a classifying space
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In his paper Construction of Universal Bundles, II, Milnor constructed a universal bundle $EG \to BG$ for any topological group $G$ using the notion of join. It is now called the Milnor (join) construction. Aside from the original paper, this construction can be found, for example, in Appendix B of Spin Geometry by Lawson & Michelsohn.