Survey on Classifying Spaces for Families of Subgroups

  title={Survey on Classifying Spaces for Families of Subgroups},
  author={Wolfgang Lueck},
  journal={arXiv: Geometric Topology},
  • 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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