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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.

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
Full Text: DOI arXiv
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