2 Se p 20 11 COMMUTING ELEMENTS , SIMPLICIAL SPACES AND FILTRATIONS OF CLASSIFYING SPACES

@inproceedings{Adem2SP,
  title={2 Se p 20 11 COMMUTING ELEMENTS , SIMPLICIAL SPACES AND FILTRATIONS OF CLASSIFYING SPACES},
  author={A. Adem and Frederick R. Cohen and E. Giese}
}
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 B(2, G) assembled from all the n–tuples of commuting elements in G. Homotopy properties of the B(q, G) are considered for finite groups… CONTINUE READING

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