Infinitely presented graphical small cancellation groups are acylindrically hyperbolic

By Dominik Gruber, Alessandro Sisto. 2014

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We prove that infinitely presented graphical Gr(7) small cancellation groups are acylindrically hyperbolic. In particular, infinitely presented classical C(7)-groups and, hence, classical C′( 1 6 )-groups are acylindrically hyperbolic. We also prove the analogous statements for the larger class of graphical small cancellation presentations over free products. We construct infinitely presented classical C′( 1 6 )-groups that provide new examples of divergence functions of groups.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ceac5508e7b8c9227eb3f3aaa1ed85c83b2ed536