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Local quasiconvexity of groups acting on small cancellation complexes. (English) Zbl 1241.20047
Summary: 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 $$\mathcal A*\mathcal B/\langle r^n\rangle$$ are coherent if $$\mathcal A$$ and $$\mathcal B$$ are coherent.

MSC:
 20F65 Geometric group theory 20E07 Subgroup theorems; subgroup growth 20E06 Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations 57M50 General geometric structures on low-dimensional manifolds
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