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There was some recent addition of pages on classifying spaces, including their cohomology, as mentioned eg here.
more references for cohomology of $B O(n)$ are also recorded at orthogonal group, here.
we should maybe make an !include
-entry for a comprehensive list of these references so that all these lists get harmonized and synchronized
Out of interest, what counts as a classifying space? The spheres as classifying spaces for cohomotopy? At classifying space we have $Cat$ as the “classifying space for categories”.
I see also there at we have a section on cohomology which includes Segal completion – table.
True. There is the traditional meaning of classifying spaces as variants of bar constructions for topological groups, classifying the corresponding principal bundles on nice enough base spaces.
That traditional meaning is often implied by default, such as in the entry that Dmitri is starting here.
But just going by the literal meaning of the words “classifying space” there can be classifying spaces for other or more general things – such as for cohomology theories — and it’s often useful to have the term be understood in this more general sense.
On the other hand, calling “Cat” a classifying space is a bit of an abuse of terminology. If one called it at least a “directed classifying space” it would make better sense.
(I have now edited at classifying space in order to clarify, see the log message there)
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