JournalsggdVol. 7, No. 3pp. 535–541

Regular elements in CAT(0) groups

  • Pierre-Emmanuel Caprace

    Université Catholique de Louvain, Belgium
  • Gašper Zadnik

    University of Ljubljana, Slovenia
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Let XX be a locally compact geodesically complete CAT(0)\mathrm{CAT}(0) space and Γ\Gamma be a discrete group acting properly and cocompactly on XX. We show that Γ\Gamma contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of XX. It follows that if XX is a product of dd factors, then Γ\Gamma contains Zd\mathbb{Z}^d.

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Pierre-Emmanuel Caprace, Gašper Zadnik, Regular elements in CAT(0) groups. Groups Geom. Dyn. 7 (2013), no. 3, pp. 535–541

DOI 10.4171/GGD/195