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Periodic flats in CAT(0) cube complexes

Michah Sageev and Daniel T Wise

Algebraic & Geometric Topology 11 (2011) 1793–1820

DOI: 10.2140/agt.2011.11.1793


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

Mathematical Subject Classification

Primary: 20E99, 20F65, 20F67


Received: 24 January 2010
Accepted: 28 January 2010
Published: 12 June 2011

Michah Sageev
Department of Mathematics
Haifa 32000
Daniel T Wise
Mathematics and Statistics
McGill University
Canada H3A 2K6