Limit groups for relatively hyperbolic groups. I: The basic tools.

DOI10.2140/agt.2009.9.1423zbMath1231.20038arXivmath/0412492OpenAlexW3104797370MaRDI QIDQ834380

Daniel Groves

Publication date: 20 August 2009

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0412492

zbMATH Keywords

limit groupsrelatively hyperbolic groupsMakanin-Razborov diagrams\(\mathbb{R}\)-trees

Mathematics Subject Classification ID

Geometric group theory (20F65) Topological methods in group theory (57M07) Hyperbolic groups and nonpositively curved groups (20F67) Groups acting on trees (20E08)

Related Items (21)

A Cartan-Hadamard type result for relatively hyperbolic groups ⋮ Complexity volumes of splittable groups ⋮ OEandW* superrigidity results for actions by surface braid groups ⋮ Aspherical manifolds, relative hyperbolicity, simplicial volume and assembly maps. ⋮ Stallings graphs for quasi-convex subgroups ⋮ Lower bound on growth of non-elementary subgroups in relatively hyperbolic groups ⋮ The structure of limit groups over hyperbolic groups ⋮ Algebraic geometry over algebraic structures. II: Foundations ⋮ Random groups do not split. ⋮ Discrete representations of finitely generated groups into PSL(2,R)${\rm PSL}(2,\mathbb {R})$ ⋮ Limit groups over coherent right-angled Artin groups ⋮ A WHITEHEAD ALGORITHM FOR TORAL RELATIVELY HYPERBOLIC GROUPS ⋮ Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups. ⋮ Simple loop conjecture for limit groups ⋮ Algebraic characterisation of relatively hyperbolic special groups ⋮ On systems of equations over free partially commutative groups ⋮ Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families ⋮ The isomorphism problem for toral relatively hyperbolic groups. ⋮ Towers and elementary embeddings in toral relatively hyperbolic groups ⋮ Limit groups for relatively hyperbolic groups. II: Makanin-Razborov diagrams. ⋮ On automorphisms and splittings of special groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Gromov's theorem on groups of polynomial growth and elementary logic
• Limit groups for relatively hyperbolic groups. II: Makanin-Razborov diagrams.
• Elementary theory of free non-abelian groups.
• Dehn filling in relatively hyperbolic groups.
• The isomorphism problem for toral relatively hyperbolic groups.
• Degenerations of the hyperbolic space
• Ergodic theory and free actions of groups on \({\mathbb{R}}\)-trees
• Groups of polynomial growth and expanding maps. Appendix by Jacques Tits
• Dynamics for rotation pseudogroups
• Structure and rigidity in hyperbolic groups. I
• Acylindrical accessibility for groups
• Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
• Combination of convergence groups.
• Diophantine geometry over groups. IV: An iterative procedure for validation of a sentence.
• Limit groups as limits of free groups.
• Diophantine geometry over groups. II: Completions, closures and formal solutions
• Diophantine geometry over groups. I: Makanin-Razborov diagrams
• Nonpositively curved 2-complexes with isolated flats.
• On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds
• Stable actions of groups on real trees
• On Hausdorff-Gromov convergence and a theorem of Paulin
• Diophantine geometry over groups. III: Rigid and solid solutions.
• Diophantine geometry over groups. V\(_1\): Quantifier elimination. I.
• Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).
• Makanin-Razborov diagrams for limit groups.
• Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups.
• Accidental parabolics and relatively hyperbolic groups.
• Actions of finitely generated groups on \(\mathbb{R}\)-trees.
• Tree-graded spaces and asymptotic cones of groups. (With an appendix by Denis Osin and Mark Sapir).
• Diophantine geometry over groups. V\(_2\): Quantifier elimination. II.
• Diophantine geometry over groups. VI: The elementary theory of a free group.
• Limits of (certain) CAT(0) groups. I: Compactification.
• Some geometric groups with rapid decay
• RELATIVELY HYPERBOLIC GROUPS
• Notes on Sela's work: Limit groups and Makanin-Razborov diagrams
• Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems
• Classifying Spaces and Boundaries for Relatively Hyperbolic Groups
• A topological characterisation of relatively hyperbolic groups
• Diophantine geometry over groups VII: The elementary theory of a hyperbolic group
• A COMBINATION THEOREM FOR RELATIVELY HYPERBOLIC GROUPS
• Relatively hyperbolic groups
• Relatively hyperbolic groups

This page was built for publication: Limit groups for relatively hyperbolic groups. I: The basic tools.