Let X be a locally compact geodesically complete CAT(0) space and Γ be a discrete group acting properly and cocompactly on X. We show that Γ contains an element acting as a hyperbolic isometry on each indecomposable de Rham factor of X. It follows that if X is a product of d factors, then Γ contains Zd.
1
Université Catholique de Louvain, Belgium
2
University of Ljubljana, Slovenia
Pierre-Emmanuel Caprace; Gašper Zadnik. Regular elements in CAT(0) groups. Groups, geometry, and dynamics, Tome 7 (2013) no. 3, pp. 535-541. doi: 10.4171/ggd/195
@article{10_4171_ggd_195,
author = {Pierre-Emmanuel Caprace and Ga\v{s}per Zadnik},
title = {Regular elements in {CAT(0)} groups},
journal = {Groups, geometry, and dynamics},
pages = {535--541},
year = {2013},
volume = {7},
number = {3},
doi = {10.4171/ggd/195},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/195/}
}
TY - JOUR
AU - Pierre-Emmanuel Caprace
AU - Gašper Zadnik
TI - Regular elements in CAT(0) groups
JO - Groups, geometry, and dynamics
PY - 2013
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EP - 541
VL - 7
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/195/
DO - 10.4171/ggd/195
ID - 10_4171_ggd_195
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%R 10.4171/ggd/195
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