Volume 4, issue 1 (2004)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
References
Forward citations
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