Geometric and Functional Analysis

, Volume 17, Issue 5, pp 1551-1620

First online:

Special Cube Complexes

  • Frédéric HaglundAffiliated withLaboratoire de Mathématiques, Université de Paris XI (Paris-Sud)
  • , Daniel T. WiseAffiliated withDept. of Math., McGill University Email author 

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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