Alejandro Adem, Frederick R. Cohen
Published 2006-03-08, updated 2006-05-19Version 2
This article records basic topological, as well as homological properties of the space of homomorphisms Hom(L,G) where L is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If L is a free abelian group of rank equal to n, then Hom(L,G) is the space of ordered n-tuples of commuting elements in G. If G=SU(2), a complete calculation of the cohomology of these spaces is given for n=2, 3. An explicit stable splitting of these spaces is also obtained, as a special case of a more general splitting.
Comments: Revised version correcting homology calculations and a few minor points
Commuting elements, simplicial spaces, and filtrations of classifying spaces
Cohomology and $K$-theory rings of the space of commuting elements in $SU(2)$
On spaces of commuting elements in Lie groups
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