# Survey on Classifying Spaces for Families of Subgroups

@article{Lueck2005SurveyOC,
title={Survey on Classifying Spaces for Families of Subgroups},
author={Wolfgang Lueck},
journal={arXiv: Geometric Topology},
year={2005},
pages={269-322}
}
• W. Lueck
• Published 19 December 2003
• Mathematics
• arXiv: Geometric Topology
We define for a topological group G and a family of subgroups $$\mathcal{F}$$ two versions for the classifying space for the family $$\mathcal{F}$$ , the G-CW-version $$E_\mathcal{F}$$ (G) and the numerable G-space version $$J_\mathcal{F}$$ (G). They agree if G is discrete, or if G is a Lie group and each element in $$\mathcal{F}$$ compact, or if $$\mathcal{F}$$ is the family of compact subgroups. We discuss special geometric models for these spaces for the family of compact open… Expand
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