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Results tagged with classifying-spaces
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user 4177
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.
5
votes
1
answer
273
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Can the set of iso classes of G-equivariant H-bundles be given by ordinary homotopy classes ...
Let $G$ be a (nice enough) topological group (actually a filtered colimit of compact Lie groups), and let $X$ be a manifold with an action (a proper one in fact) by a Lie group $H$. Let $X//H := (X\ti …
- 35.5k
6
votes
1
answer
406
views
Cohomology of BG, G non-connected Lie group, and spectral sequence relating to classifying s...
Suppose $G$ is a Lie group, with $\pi_0(G)$ not necessarily finite, but might as well assume $G_0$, the connected component of the identity, is compact.
In the case that $\pi_0(G)$ is finite, then we …
- 35.5k
8
votes
1
answer
264
views
When does $BG \to BA$ loop to a homomorphism?
If I have a compact connected Lie group $G$ and a (relatively nice) simply-connected topological abelian group $A$, when is it the case that a given $f\colon BG \to BA$ loops to a (continuous) homomor …
- 35.5k
8
votes
1
answer
684
views
For which G is BLG weak homotopy equivalent to LBG?
Let $G$ be a (Edit: path-)connected topological group. Under what additional hypotheses on $G$ is it true that $LBG$ is a classifying space for $LG$? (or, I guess equivalently, when is $LBG \sim BLG$? …
- 35.5k
4
votes
2
answers
314
views
Low dimensional integral cohomology of $BPSO(4n)$
Toda has calculated the $\mathbb{Z}/2$‐cohomology ring of $BPSO(4n+2)$, and also gave the simple exceptional calculation of the $\mathbb{Z}/2$‐cohomology of $BPSO(4)$, in
Hiroshi Toda, Cohomology of …
- 35.5k