Algebraic and Geometric Topology 4 (2004), paper no. 28, pages 603-622.

Foldable cubical complexes of nonpositive curvature

Xiangdong Xie

Abstract. 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 dim X=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.

Keywords. Rank one geodesic, cubical complex, nonpositive curvature

AMS subject classification. Primary: 20F65, 20F67. Secondary: 53C20.

DOI: 10.2140/agt.2004.4.603

E-print: arXiv:math.MG/0409067

Submitted: 19 September 2003. (Revised: 14 May 2004.) Accepted: 2 August 2004. Published: 20 August 2004.

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Xiangdong Xie
Department of Mathematical Sciences, University of Cincinnati
Cincinnati, OH 45221, USA
Email: xiexg@ucmail.uc.edu

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