The cohomology of 𝐵𝑆𝑂_{𝑛} and 𝐵𝑂_{𝑛} with integer coefficients

Brown, Edgar H.

doi:10.1090/S0002-9939-1982-0652459-1

The cohomology of $B\textrm {SO}_{n}$ and $B\textrm {O}_{n}$ with integer coefficients
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by Edgar H. Brown

Proc. Amer. Math. Soc. 85 (1982), 283-288

DOI: https://doi.org/10.1090/S0002-9939-1982-0652459-1

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Abstract:

The cohomology rings of $BS{O_n}$ and $B{O_n}$, with integer coefficients, are given by generators and relations expressed in terms of characteristic classes.

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The integral cohomology rings of the real Grassmannians