Geometric and Functional Analysis

, Volume 17, Issue 5, pp 1551–1620

Special Cube Complexes

Article

Abstract.

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 complexes right-angled Artin groups residual finiteness 

AMS Mathematics Subject Classification:

53C23 20F36 20F55 20F67 20F65 20E26 

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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

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