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Created page for BU(n), the classifying space of the unitary group U(n). (See discussion on Stiefel-Whitney class.) There is still a lot to add though.
There seems to have been a glitch in the last sentence (“limit” instead of “colimit” and a sudden appearance if $SU(n)$ instead of $\mathrm{U}(n)$). I have fixed it and added a link to stable unitary group.
Added the simplest classifying space $B U(1)\cong\mathbb{C}P^\infty$ and its classification of $U(1)$ principal bundles. (A section about the general classification will follow soon.) Also linked the Wikipedia page Classifying space for U(n).
Edit: As a link including “)” can’t be linked due to disrupting the
environment, I have created a redirect from “Classifying space for unitary group”.
Added reference for definition in Milnor & Stasheff. Added connection to characteristic classes. (I plan to create the page for balanced product in the future.) Also linked pages of BSO(n) and BSU(n), which I will create either today or tomorrow.
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