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Inventiones mathematicae

, Volume 150, Issue 2, pp 219–235 | Cite as

Van Kampen’s embedding obstruction for discrete groups

  • Mladen Bestvina
  • Michael Kapovich
  • Bruce Kleiner

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 ℝ2 n −1.

Keywords

Manifold Free Group Discrete Group Contractible Manifold Nonabelian Free Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Mladen Bestvina
    • 1
  • Michael Kapovich
    • 1
  • Bruce Kleiner
    • 2
  1. 1.Department of Mathematics, University Utah, Salt Lake City, UT 84112-0090, USAUS
  2. 2.Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USAUS

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