Cubulating small cancellation groups

• DOI: 10.1007/s00039-004-0454-y
• Publication Date: 2004-04-20T03:21:03Z
• Authors: Daniel T. Wise
• Keywords: Codimension; Finitely generated group

We study the B(6) and B(4)-T(4) small cancellation groups. These classes include the usual C’(1/6) and C’(1/4)-T(4) metric small cancellation groups. We show that every finitely presented B(4)-T(4) or word-hyperbolic B(6) group acts properly discontinuously and cocompactly on a CAT(0) cube complex. We show that finitely generated infinite B(6) and B(4)-T(4) groups have codimension 1 subgroups and thus do not have property (T). We show that a finitely presented B(6) group is wordhyperbolic if and only if it contains no $$ \mathbb{Z} \times \mathbb{Z} $$ subgroup.