In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space
Rinfty
The cohomology ring of
\operatorname{BO}(n)
Z2
| *(\operatorname{BO}(n);Z | |
| H | |
| 2) =Z |
2[w1,\ldots,wn].
The canonical inclusions
\operatorname{O}(n)\hookrightarrow\operatorname{O}(n+1)
\operatorname{BO}(n)\hookrightarrow\operatorname{BO}(n+1)
\operatorname{O} :=\limn → infty\operatorname{O}(n);
\operatorname{BO} :=\limn → infty\operatorname{BO}(n).
\operatorname{BO}
\operatorname{O}