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Results tagged with classifying-spaces
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user 391
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.
18
votes
cohomology of BG, G compact Lie group
Here's the argument I know that avoids spectral sequences, based on the
little-known space $G/N(T)$.
In between $T$ and $G$ is $N(T)$. Note that $EG$ "is an" $ET$ and $EN(T)$,
since it's contractib …
- 27.9k
1
vote
Accepted
Elementary question: Intuition for equivariant cohomology
I'm guessing that, unstated, $M,G$ are finite-dimensional and $G$ is connected Lie.
Then $H^*(M/G)$ vanishes for $* \gg 0$, but $H^*_G$ is positively graded, so $H^*(M/G)$ must be a torsion module. …
- 27.9k