FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

DOI10.1142/S0218196704001682zbMath1094.20022arXivmath/0203015OpenAlexW1991311317MaRDI QIDQ5692233

Richard Weidmann, Ilya Kapovich

Publication date: 27 September 2005

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203015

zbMATH Keywords

numbers of conjugacy classesword hyperbolic groupsfree productsfundamental groupsGromov hyperbolic spaceshyperbolic three-manifoldsNielsen equivalencelocally quasiconvex subgroupsalmost torsion-free groupsfreely indecomposable finitely generated subgroups

Mathematics Subject Classification ID

Conjugacy classes for groups (20E45) Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Hyperbolic groups and nonpositively curved groups (20F67)

Related Items

Nielsen equivalence in Fuchsian groups, A zero-one law for random subgroups of some totally disconnected groups, Kleinian groups and the rank problem., Conjugacy of 2-spherical subgroups of Coxeter groups and parallel walls., Fully irreducible automorphisms of the free group via Dehn twisting in \(\sharp_k(S^2\times S^1)\), Ends of Schreier graphs of hyperbolic groups, Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups., Acylindrical accessibility for groups acting on \(\mathbb{R}\)-trees., Rank and Nielsen equivalence in hyperbolic extensions

Cites Work

• Covering theory for graphs of groups
• A combination theorem for negatively curved groups
• Géométrie et théorie des groupes. Les groupes hyperboliques de Gromov. (Geometry and group theory. The hyperbolic groups of Gromov)
• Geometric finiteness and rationality
• Structure and rigidity in (Gromov) hyperbolic groups and discrete groups in rank \(1\) Lie groups. II
• Nielsen methods and groups acting on hyperbolic spaces
• Coxeter groups, 2-completion, perimeter reduction and subgroup separability.
• The image of a group in a hyperbolic group
• Hyperbolic elements in negatively curved groups
• Distinguished subgroups and quotients of hyperbolic groups
• A covering theorem for hyperbolic 3-manifolds and its applications
• Introduction to group theory. Translated from the Russian. With a new chapter.
• Towers, ladders and the B. B. Newman Spelling Theorem
• Greenberg's Theorem for Quasiconvex Subgroups of Word Hyperbolic Groups
• Subgroups of small Cancellation Groups
• Generic properties of finitely presented groups and howson's theorem
• Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion
• THE COMBINATION THEOREM AND QUASICONVEXITY
• ON SMALL CANCELLATION k-GENERATED GROUPS WITH (k-1)-GENERATED SUBGROUPS ALL FREE
• Hyperbolic manifolds and discrete groups
• Quasi-convex groups of isometries of negatively curved spaces