Special Cube Complexes

• DOI: 10.1007/s00039-007-0629-4
• Publication Date: 2007-10-18T14:02:53Z
• Authors: Frédéric Haglund; Daniel T. Wise
• Keywords: Cube (algebra); Quasiconvex function; Sequence (biology); Cube root; Special linear group

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.