 Classifying space of a discrete group (source code)

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= Classifying space of a discrete group
{title2=$BG=K(G,1)$}

Give a discrete group $G$ a contractible free <CW complex> $EG$. The quotient $BG=EG/G$ has <universal cover> $EG$, so it has <fundamental group> $G$ and no higher <homotopy groups>. It is thus an <Eilenberg–MacLane space> $K(G,1)$, even when $G$ is nonabelian. The cohomology of $BG$ with the appropriate local coefficients computes <group cohomology>.

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