Commuting elements, simplicial spaces, and filtrations of classifying spaces

Details Commuting elements, simplicial spaces, and filtrations of classifying spaces Commuting elements, simplicial spaces, and filtrations of classifying spaces

2008-12-31

arxiv.org/abs/0901.0137v4

Mathematics

Algebraic Topology

Revised version of original manuscript, to appear in Mathematical Proceedings of the Cambridge Philosophical Society

Scientific paper

Using spaces of homomorphisms and the descending central series of the free groups, simplicial spaces are constructed for each integer q>1 and every topological group G, with realizations B(q,G) that 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. Cohomology calculations are provided for compact Lie groups. The spaces B(2,G) are described in detail for transitively commutative groups.

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