Geometric and Functional Analysis

, Volume 17, Issue 5, pp 1551–1620

Special Cube Complexes


DOI: 10.1007/s00039-007-0629-4

Cite this article as:
Haglund, F. & Wise, D.T. GAFA Geom. funct. anal. (2008) 17: 1551. doi:10.1007/s00039-007-0629-4


We introduce and examine a special class of cube complexes. We show that special cube-complexes virtually admit local isometries to the standard 2-complexes of naturally associated right-angled Artin groups. Consequently, special cube-complexes have linear fundamental groups. In the word-hyperbolic case, we prove the separability of quasiconvex subgroups of fundamental groups of special cube-complexes. Finally, we give a linear variant of Rips’s short exact sequence.

Keywords and phrases:

CAT(0) cube complexesright-angled Artin groupsresidual finiteness

AMS Mathematics Subject Classification:


Copyright information

© Birkhaeuser 2007

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Paris XI (Paris-Sud)OrsayFrance
  2. 2.Dept. of Math.McGill UniversityMontrealCanada