We study finite foldable cubical complexes of nonpositive curvature (in the sense of A D Alexandrov). We show that such a complex admits a graph of spaces decomposition. It is also shown that when , contains a closed rank one geodesic in the –skeleton unless the universal cover of is isometric to the product of two CAT(0) cubical complexes.
"Foldable cubical complexes of nonpositive curvature." Algebr. Geom. Topol. 4 (1) 603 - 622, 2004. https://doi.org/10.2140/agt.2004.4.603