### Abstract

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.

Original language | English |
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Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Early online date | 9 Mar 2020 |

DOIs | |

Publication status | E-pub ahead of print - 9 Mar 2020 |

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### ASJC Scopus subject areas

- Mathematics(all)