#### Volume 11, issue 3 (2011)

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Periodic flats in $\mathrm{CAT}(0)$ cube complexes

### Michah Sageev and Daniel T Wise

Algebraic & Geometric Topology 11 (2011) 1793–1820
##### Abstract

We show that the flat closing conjecture is true for groups acting properly and cocompactly on a CAT(0) cube complex when the action satisfies the cyclic facing triple property. For instance, this property holds for fundamental groups of 3–manifolds that act freely on CAT(0) cube complexes.

 In memory of Bob Brooks
##### Keywords
CAT(0) cubical complex, word-hyperbolic group, torus, flat closing
##### Mathematical Subject Classification 2000
Primary: 20E99, 20F65, 20F67
##### Publication
Received: 24 January 2010
Accepted: 28 January 2010
Published: 12 June 2011
##### Authors
 Michah Sageev Department of Mathematics Technion Haifa 32000 Israel Daniel T Wise Mathematics and Statistics McGill University Montreal Quebec Canada H3A 2K6