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Cubulating small cancellation groups
Authors:Daniel T Wise
Institution:(1) Math. & Stats., McGill University, Montreal, Quebec, H3A 2K6, Canada
Abstract:We study the B(6) and B(4)-T(4) small cancellation groups. These classes include the usual Crsquo(1/6) and Crsquo(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.
Keywords:((no ))
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