Commuting Elements and Spaces of Homomorphisms

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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.
Revised version correcting homology calculations and a few minor points

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Algebraic Topology, 20F36; 55N15, 55R50

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http://salesiana.dossiersoluciones.com/handle/123456789/110107

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0603197
 http://arxiv.org/abs/math/0603197

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arXiv