Salvetti complex
= Salvetti complex
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{title2=$S_\Gamma$}
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The Salvetti complex $S_\Gamma$ has one vertex, one oriented loop for each vertex of $\Gamma$, and an $n$-torus cubulated by one $n$-cube for every $n$-clique of $\Gamma$. It is nonpositively curved and $\pi_1S_\Gamma\cong A_\Gamma$.