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Special Cube Complexes

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.

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Correspondence to Daniel T. Wise.

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Research supported by grants from NSERC and FCAR.

Received: October 2005, Accepted: September 2006

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Haglund, F., Wise, D.T. Special Cube Complexes. GAFA Geom. funct. anal. 17, 1551–1620 (2008). https://doi.org/10.1007/s00039-007-0629-4

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Keywords and phrases:

  • CAT(0) cube complexes
  • right-angled Artin groups
  • residual finiteness

AMS Mathematics Subject Classification:

  • 53C23
  • 20F36
  • 20F55
  • 20F67
  • 20F65
  • 20E26