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Let Γ q denote the q-th stage of the descending central series of the free group on n generators F n. For each q ≥ 2 and every topological group G, a simplicial space B * (q, G) is constructed where B n (q, G) = Hom(F n /Γ q , G) and the realizations B(q, G) = |B * (q, G)| filter the classifying space BG. In particular for q = 2 this yields a single space(More)
Let Γ q denote the q-th stage of the descending central series of the free group on n generators F n. For each q ≥ 2 and every topological group G, a simplicial space B * (q, G) is constructed where B n (q, G) = Hom(F n /Γ q , G) and the realizations B(q, G) = |B * (q, G)| filter the classifying space BG. Homotopy properties of B(q, G) are considered for(More)
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