Algebraic & Geometric Topology

Foldable cubical complexes of nonpositive curvature

Xiangdong Xie

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We study finite foldable cubical complexes of nonpositive curvature (in the sense of A D Alexandrov). We show that such a complex X admits a graph of spaces decomposition. It is also shown that when dimX=3, X contains a closed rank one geodesic in the 1–skeleton unless the universal cover of X is isometric to the product of two CAT(0) cubical complexes.

Article information

Algebr. Geom. Topol., Volume 4, Number 1 (2004), 603-622.

Received: 19 September 2003
Revised: 14 May 2004
Accepted: 2 August 2004
First available in Project Euclid: 21 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

rank one geodesic cubical complex nonpositive curvature


Xie, Xiangdong. Foldable cubical complexes of nonpositive curvature. Algebr. Geom. Topol. 4 (2004), no. 1, 603--622. doi:10.2140/agt.2004.4.603.

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