Limit groups as limits of free groups.

DOI10.1007/BF02773526zbMath1103.20026arXivmath/0401042OpenAlexW2945209112MaRDI QIDQ1781931

Vincent Guirardel, Christophe Champetier

Publication date: 9 June 2005

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0401042

zbMATH Keywords

finitely generated groups marked groups universal theories limit groups fully residually free groups

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Model-theoretic algebra (03C60) Generators, relations, and presentations of groups (20F05) Topological methods in group theory (57M07) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Residual properties and generalizations; residually finite groups (20E26)

Related Items

Magnus pairs in, and free conjugacy separability of, limit groups, Note on the Cantor–Bendixson Rank of Limit Groups, LIMITS OF METABELIAN GROUPS, Limit groups for relatively hyperbolic groups. I: The basic tools., Generalized Grigorchuk’s overgroups as points in the space of marked 8-generated groups, A gluing theorem for negatively curved complexes, Limit groups and groups acting freely on \(\mathbb{R}^n\)-trees., OEandW* superrigidity results for actions by surface braid groups, Infinite presentability of groups and condensation, On the isolated points in the space of groups., Normalisers in limit groups., Asymptotic invariants of finitely generated algebras. A generalization of Gromov's quasi-isometric viewpoint., Relatively hyperbolic groups are \(C^*\)-simple., On the Cantor-Bendixson rank of the Grigorchuk group and the Gupta-Sidki 3 group, Profinite extensions of centralizers and the profinite completion of limit groups, Effective construction of covers of canonical Hom-diagrams for equations over torsion-free hyperbolic groups, Algebraic geometry over algebraic structures. II: Foundations, Krull dimension of solvable groups., The Borel conjecture for hyperbolic and CAT(0)-groups, Free orbits for minimal actions on the circle, Normal subgroups in limit groups of prime index, Compactifications and algebraic completions of limit groups, Limit groups over coherent right-angled Artin groups, Approximating nonabelian free groups by groups of homeomorphisms of the real line, Limits of relatively hyperbolic groups and Lyndon's completions., Krull dimension for limit groups., Limit groups over coherent right-angled Artin groups are cyclic subgroup separable, Connected components of the compactification of representation spaces of surface groups, Group cocycles and the ring of affiliated operators, Some topics in the dynamics of group actions on rooted trees., Locally infinite graphs and symmetries, On the Cantor-Bendixson rank of metabelian groups., Limits of Baumslag-Solitar groups and dimension estimates in the space of marked groups., On approximation properties of semidirect products of groups, On group-theoretic models of randomness and genericity., The space of minimal structures, Algebraic and definable closure in free groups, Elementary equivalence vs. commensurability for hyperbolic groups, Unnamed Item, Estimates of Minkowski dimensions in the space of marked groups., Volume gradients and homology in towers of residually-free groups, ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS, Isomorphism of finitely generated solvable groups is weakly universal., A sofic group away from amenable groups., Subgroups of direct products of limit groups., Amenable groups without finitely presented amenable covers, Free limits of Thompson's group \(F\)., Algebraic characterisation of relatively hyperbolic special groups, Limits of generalized quaternion groups, The free group of rank 2 is a limit of Thompson's group \(F\)., The stable set of a self-map, A Magnus extension for locally indicable groups, Surface groups in the group of germs of analytic diffeomorphisms in one variable, Limits of dihedral groups., Ordering the space of finitely generated groups, Groups and Embeddings inSL(2, ℂ), On Property (FA) for wreath products, A Magnus theorem for some amalgamated products, Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups, Homomorphisms to acylindrically hyperbolic groups I: Equationally noetherian groups and families, On decidability of amenability in computable groups, Scl in graphs of groups, Limits of (certain) CAT(0) groups. I: Compactification., Limit groups over partially commutative groups and group actions on real cubings, Descriptive complexity of subsets of the space of finitely generated groups, Magnus embedding and algorithmic properties of groups 𝐹/𝑁^{(𝑑)}, From local to global conjugacy of subgroups of relatively hyperbolic groups

Cites Work