Commuting Elements and Spaces of Homomorphisms

Alejandro Adem; Frederick R. Cohen

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Commuting Elements and Spaces of Homomorphisms

Alejandro Adem·Frederick R. Cohen

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Abstract

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.

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BibTeX RIS

Alejandro Adem, Frederick R. Cohen. 2006-05-19. Commuting Elements and Spaces of Homomorphisms. https://arxiv.org/abs/math/0603197

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