Commuting elements and spaces of homomorphisms

• Autores: Alejandro Adem, Frederick R. Cohen
• Localización: Mathematische Annalen, ISSN 0025-5831, Vol. 338, Nº. 3, 2007, págs. 587-626
• Idioma: inglés
• DOI: 10.1007/s00208-007-0089-z
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• Resumen

  • This article records basic topological, as well as homological properties of the space of homomorphisms Hom(p,G) where p is a finitely generated discrete group, and G is a Lie group, possibly non-compact. If p is a free abelian group of rank equal to n, then Hom(p, 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.