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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