Van Kampen’s embedding obstruction for discrete groups

@article{Bestvina2000VanKE,
  title={Van Kampen’s embedding obstruction for discrete groups},
  author={Mladen Bestvina and Michael Kapovich and Bruce Kleiner},
  journal={Inventiones mathematicae},
  year={2000},
  volume={150},
  pages={219-235}
}
Abstract.We give a lower bound to the dimension of a contractible manifold on which a given group can act properly discontinuously. In particular, we show that the n-fold product of nonabelian free groups cannot act properly discontinuously on ℝ2n−1. 
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A rink-type roller skate is provided with a plastic sole plate. To mount a toe stop on the skate, a novel bushing is embedded in the sole plate. The bushing has relatively small diameter ends and a
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