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Results tagged with classifying-spaces
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user 1345
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.
7
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Accepted
Odd homotopy group of $BU(m)$
From the long exact sequence of homotopy groups associated to the fibration $U\to EU\to BU$, one has that $\pi_{2k+1}(BU(m))=\pi_{2k}(U(m))$ (since $EU$ is contractible, and for $k>0$). From the proof …
- 68.9k
22
votes
Why isn't $BG$ a group, for $G$ not abelian?
A simple answer for why $BG$ is not a group when $G$ is discrete is that $BG=K(G,1)$, so $\pi_1(BG)=G$. However, if $K(G,1)$ were a topological group, then $\pi_1(K(G,1))=G$ must be abelian. This is p …
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