- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
7
2013
3
Regular elements in CAT(0) groups
Pierre-Emmanuel
Caprace
Université Catholique de Louvain, LOUVAIN-LA-NEUVE, BELGIUM
Gašper
Zadnik
University of Ljubljana, LJUBLJANA, SLOVENIA
CAT(0) group, regular elements, flat closing conjecture
Let $X$ be a locally compact geodesically complete $\mathrm{CAT}(0)$ space and $\Gamma$ be a discrete group acting properly and cocompactly on $X$. We show that $\Gamma$ 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 $\Gamma$ contains $\mathbb{Z}^d$.
Group theory and generalizations
535
541
10.4171/GGD/195
http://www.ems-ph.org/doi/10.4171/GGD/195