Algebraic & Geometric Topology Volume 11, issue 3 (2011)

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

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Keywords

CAT(0) cubical complex, word-hyperbolic group, torus, flat closing

Mathematical Subject Classification

Primary: 20E99, 20F65, 20F67

References

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