A combination theorem for combinatorially non-positively curved complexes of hyperbolic groups

Alexandre Martin, Damian Osajda

Research output: Contribution to journalArticle


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 languageEnglish
JournalMathematical Proceedings of the Cambridge Philosophical Society
Early online date9 Mar 2020
Publication statusE-pub ahead of print - 9 Mar 2020


ASJC Scopus subject areas

  • Mathematics(all)

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