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Results tagged with classifying-spaces
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user 290
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.
23
votes
Accepted
Why isn't $BG$ a group, for $G$ not abelian?
The classifying space functor may be a monoidal functor out of $\text{Grp}$, but nonabelian groups aren't group objects in $\text{Grp}$. (The group objects in $\text{Grp}$ are precisely the abelian gr …
- 118k
12
votes
Accepted
classifying space of orthogonal groups
$BO$ is the connected component of the zeroth space of a spectrum called the real K-theory spectrum. This spectrum represents a cohomology theory, namely real K-theory, and this means that $BO$ has mu …
- 118k
16
votes
Accepted
quotient space of Eilenberg-MacLane space
Suppose a group $H$, not necessarily finite, acts on an Eilenberg-MacLane space $BN$. The homotopy quotient $BN/H$ (which agrees with the ordinary quotient if the action of $H$ is free) fits into a fi …
- 118k