Foldable cubical complexes of nonpositive curvature

Details Foldable cubical complexes of nonpositive curvature Foldable cubical complexes of nonpositive curvature

2004-09-05

arxiv.org/abs/math/0409067v1

Algebr. Geom. Topol. 4 (2004) 603-622

Mathematics

Metric Geometry

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-28.abs.html

Scientific paper

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.

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