Local Quasiconvexity of Groups acting on Small Cancellation Complexes

Abstract

Given a group acting cellularly and cocompactly on a simply-connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the "perimeter method". As an application, we show that high-powered one-relator products $A \ast B / \nclose{r^n}$ are coherent if $A$ and $B$ are coherent.

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• Coherence and Negative Sectional Curvature in Complexes of Groups
• The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups