Relative quasiconvexity using fine hyperbolic graphs
Copyright policy )Relative quasiconvexity using fine hyperbolic graphs
We provide a new and elegant approach to relative quasiconvexity for relatively hyperbolic groups in the context of Bowditch's approach to relative hyperbolicity using cocompact actions on fine hyperbolic graphs. Our approach to quasiconvexity generalizes the other definitions in the literature that apply only for countable relatively hyperbolic groups. We also provide an elementary and self-contained proof that relatively quasiconvex subgroups are relatively hyperbolic.
21 pages, 6 figures. New section on fine graphs. Version to appear in AGT
- McGill University Canada
- McMaster University Canada
20F06, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, 20F65, 20F67, 20F06, relatively hyperbolic groups, 20F67, quasiconvex subgroups, Subgroup theorems; subgroup growth, Group Theory (math.GR), Cancellation theory of groups; application of van Kampen diagrams, Hyperbolic groups and nonpositively curved groups, fine graphs, hyperbolic group, fine graph, relatively hyperbolic group, quasiconvex subgroup, FOS: Mathematics, 20F65, Geometric group theory, Mathematics - Group Theory
20F06, Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations, 20F65, 20F67, 20F06, relatively hyperbolic groups, 20F67, quasiconvex subgroups, Subgroup theorems; subgroup growth, Group Theory (math.GR), Cancellation theory of groups; application of van Kampen diagrams, Hyperbolic groups and nonpositively curved groups, fine graphs, hyperbolic group, fine graph, relatively hyperbolic group, quasiconvex subgroup, FOS: Mathematics, 20F65, Geometric group theory, Mathematics - Group Theory
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