Foldable cubical complexes of nonpositive curvature

Xie, Xiangdong

doi:10.2140/agt.2004.4.603

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Foldable cubical complexes of nonpositive curvature

Xiangdong Xie

Algebraic & Geometric Topology 4 (2004) 603–622

DOI: 10.2140/agt.2004.4.603

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 $dim X = 3$ , $X$ 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

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

Volume 4, issue 1 (2004)