Algebraic & Geometric Topology

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

Michah Sageev and Daniel T Wise

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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.

Article information

Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1793-1820.

Received: 24 January 2010
Accepted: 28 January 2010
First available in Project Euclid: 19 December 2017

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Zentralblatt MATH identifier

Primary: 20E99: None of the above, but in this section 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups

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


Sageev, Michah; Wise, Daniel T. Periodic flats in $\mathrm{CAT}(0)$ cube complexes. Algebr. Geom. Topol. 11 (2011), no. 3, 1793--1820. doi:10.2140/agt.2011.11.1793.

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