Algebraic & Geometric Topology

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

Michah Sageev and Daniel T Wise

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715246

Digital Object Identifier
doi:10.2140/agt.2011.11.1793

Mathematical Reviews number (MathSciNet)
MR2821442

Zentralblatt MATH identifier
1272.20048

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.agt/1513715246


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