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Results tagged with classifying-spaces
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user 43054
The classifying space BG of a group G classifies principal G-bundles, in that homotopy classes of maps [X, BG] are naturally identified with isomorphism classes of principal G-bundles P ⭢ X.
11
votes
Accepted
Map from a classifying space to a stack
You're almost there! The problem is that, as you've surmised, the group $\mathrm{Aut}(x)$ does not capture enough of the geometric structure of $G$. But that's easily solved:
For every $x\in X$ we ca …
- 16.5k
6
votes
A fibration of classifying spaces
By functoriality there is a map $BG\to B(G/N)$. Let $X$ to be its homotopy fiber. Then you can get a fiber sequence
$\Omega X \to G \to G/N \to X \to BG \to B(G/N)$
using the fact that $\Omega BG = …
- 16.5k