Commuting Elements and Spaces of Homomorphisms
代数拓扑
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0603197,
title = {Commuting Elements and Spaces of Homomorphisms},
author = {Alejandro Adem and Frederick R. Cohen},
journal= {arXiv preprint arXiv:math/0603197},
year = {2007}
}
备注
Revised version correcting homology calculations and a few minor points