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Foldable cubical complexes of nonpositive curvature

Xiangdong Xie

Algebraic & Geometric Topology 4 (2004) 603–622

arXiv: math.MG/0409067

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 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.

Keywords
rank one geodesic, cubical complex, nonpositive curvature
Mathematical Subject Classification 2000
Primary: 20F65, 20F67
Secondary: 53C20
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Publication
Received: 19 September 2003
Revised: 14 May 2004
Accepted: 2 August 2004
Published: 20 August 2004
Authors
Xiangdong Xie
Department of Mathematical Sciences
University of Cincinnati
Cincinnati OH 45221
USA