Geodesic
Foldable cubical complexes of nonpositive curvature
Xie, Xiangdong1
1Department of Mathematical Sciences, University of Cincinnati, Cincinnati OH 45221, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 603-622
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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.

DOI : 10.2140/agt.2004.4.603
Keywords: rank one geodesic, cubical complex, nonpositive curvature

Xie, Xiangdong  1

1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati OH 45221, USA 
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Xie, Xiangdong. Foldable cubical complexes of nonpositive curvature. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 603-622. doi: 10.2140/agt.2004.4.603

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