aspherical space

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aspherical space

Definition: An aspherical space $X$ is anything of the homotopy type $K(\pi_1 X, 1)$ , i.e. $\pi_k(X) = 0$ for $k\geq 2$ .

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group cohomology

If $X$ is an aspherical space, then $H^k_{\mathrm{sing}}(X;{\mathcal{F}}) \cong H^k_{\mathsf{Grp}}(\pi_1 X; {\mathcal{F}}_x)$ where ${\mathcal{F}}$ is a local system.

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