4
votes
1answer
68 views

Cohomology of $\Bbb CP^{\infty}=BU_1, BU_2,\dots$ : A reference request

Where can I find the calculation of the cohomology rings of the classifying spaces $BU_n,~BO_n$ and $BO,~BU$? I took a class where extensive use was made of these cohomology rings, but I missed the ...
0
votes
0answers
66 views

classifying space of $p$-group

I want to know a model for the classifying space of a finite $p$-group $P$ (say of order $p^n$) and the mod $p$ cohomology algebra of $P$. In particular, what is the classifying space and mod $p$ ...
11
votes
1answer
274 views

What functor does $K(G, 1)$ represent for nonabelian $G$?

For $G$ an abelian group, the Eilenberg-Maclane space $K(G, n)$ represents singular cohomology $H^n(-; G)$ with coefficients in $G$ on the homotopy category of CW-complexes. If $n > 1$, then $G$ ...