Peripheral splittings of groups

DOI10.1090/S0002-9947-01-02835-5zbMath1037.20041OpenAlexW1578915963MaRDI QIDQ2723464

Brian H. Bowditch

Publication date: 5 July 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02835-5

zbMATH Keywords

graphs of groupsrelatively hyperbolic groupsperipheral subgroupsmaximal parabolic subgroupsglobal cut points

Mathematics Subject Classification ID

Geometric group theory (20F65) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items

Piecewise visual, linearly connected metrics on boundaries of relatively hyperbolic groups ⋮ Connectedness properties of limit sets ⋮ RELATIVELY HYPERBOLIC GROUPS ⋮ Pretrees and arborescent convexities ⋮ Vertex finiteness for splittings of relatively hyperbolic groups ⋮ Nonhyperbolic Coxeter groups with Menger boundary ⋮ Dehn fillings and elementary splittings ⋮ Deciding isomorphy using Dehn fillings, the splitting case ⋮ Detecting free splittings in relatively hyperbolic groups ⋮ Detecting geometric splittings in finitely presented groups ⋮ A list of applications of Stallings automata ⋮ The conjugacy problem for relatively hyperbolic groups. ⋮ RELATIONS BETWEEN VARIOUS BOUNDARIES OF RELATIVELY HYPERBOLIC GROUPS ⋮ FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM ⋮ Local cut points and splittings of relatively hyperbolic groups ⋮ Boundaries of Dehn fillings ⋮ Relative hyperbolicity and Artin groups. ⋮ On groups with \(S^2\) Bowditch boundary ⋮ Connectedness properties and splittings of groups with isolated flats ⋮ The relative hyperbolicity and manifold structure of certain right-angled Coxeter groups ⋮ PARABOLIC GROUPS ACTING ON ONE-DIMENSIONAL COMPACT SPACES ⋮ The isomorphism problem for toral relatively hyperbolic groups. ⋮ Bootstrapping in convergence groups. ⋮ Pretrees and the shadow topology ⋮ QUASI-ISOMETRIES, BOUNDARIES AND JSJ-DECOMPOSITIONS OF RELATIVELY HYPERBOLIC GROUPS

Cites Work

• The accessibility of finitely presented groups
• Boundaries of geometrically finite groups
• Left cells in the affine Weyl group of type \(\widetilde F_4\)
• Geometrical finiteness with variable negative curvature
• Cutting up graphs
• Bounding the complexity of simplicial group actions on trees
• RELATIVELY HYPERBOLIC GROUPS
• The Boundary of Negatively Curved Groups
• Conical limit points and uniform convergence groups
• Connectedness properties of limit sets
• Treelike structures arising from continua and convergence groups
• Relations related to betweenness: their structure and automorphisms
• Groups Acting on Protrees
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