×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] B.H. Bowditch, Relatively hyperbolic groups, preprint, 1999.
[2] Duncan, A.J.; Howie, James, Spelling theorems and cohen – lyndon theorems for one-relator products, J. pure appl. algebra, 92, 2, 123-136, (1994) · Zbl 0847.20023
[3] Duncan, Andrew J.; Howie, James, One relator products with high-powered relators, (), 48-74 · Zbl 0820.20030
[4] Haglund, Frédéric, LES polyèdres de Gromov, C. R. acad. sci., Paris I, 313, 9, 603-606, (1991) · Zbl 0749.52011
[5] Hruska, G. Christopher; Wise, Daniel T., Towers, ladders and the B.B. Newman spelling theorem, J. aust. math. soc., 71, 1, 53-69, (2001) · Zbl 0995.20018
[6] Kampen, Egbert R. Van, On some lemmas in the theory of groups, Amer. J. math., 55, 1-4, 268-273, (1933) · Zbl 0006.39204
[7] Eduardo Martínez-Pedroza, On quasiconvexity and relatively hyperbolic structures on groups, preprint, 2008.
[8] Eduardo Martínez-Pedroza, Daniel T. Wise, Relative quasiconvexity using fine hyperbolic graphs, Algebr. Geom. Topol. (in press). · Zbl 1229.20038
[9] McCammond, J. P.; Wise, Daniel T., Coherence, local quasiconvexity, and the perimeter of 2-complexes, Geom. funct. anal., 15, 4, 859-927, (2005) · Zbl 1087.20024
[10] McCammond, Jonathan P.; Wise, Daniel T., Fans and ladders in small cancellation theory, Proc. London math. soc. (3), 84, 3, 599-644, (2002) · Zbl 1022.20012
[11] Wise, Daniel T., The residual finiteness of negatively curved polygons of finite groups, Invent. math., 149, 3, 579-617, (2002) · Zbl 1040.20024
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.