We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such complexes include for instance weakly systolic complexes and C'(1/6) small cancellation polygonal complexes. Our proof involves constructing a potential Gromov boundary for the resulting groups and analyzing the dynamics of the action on the boundary in order to use Bowditch's characterisation of hyperbolicity. A key ingredient is the introduction of a combinatorial property that implies a weak form of non-positive curvature, and which holds for large classes of complexes.As an application, we study the hyperbolicity of groups obtained by small cancellation over a graph of hyperbolic groups.
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Early online date||9 Mar 2020|
|Publication status||E-pub ahead of print - 9 Mar 2020|
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