Limit groups as limits of free groups
By Christophe Champetier, Vincent Guirardel. 2005
157 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c339ee34fb596121eb6c5d75d10b55fe12b7d60b
How researchers see this paper
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In Geometry and Topology
- Alexei G. Myasnikov
- W. Lück
- Arthur Bartels
- Olga Kharlampovich
- Martin R. Bridson
- Henry Wilton
- D. Groves
- Michael Hull
In Mathematical Physics
- Arthur Bartels
- W. Lück
- Alexei G. Myasnikov
- Martin R. Bridson
- Olga Kharlampovich
- Henry Wilton
- Michael Hull
- V. Kleptsyn
Citations in the corpus
- Small cancellation in acylindrically hyperbolic groups (2013, methodology): “. of G, lim n→∞ (G,Xn) = (H,X) where this limit is being taken in some fixed Gk. In this situation, it is not hard to show that the universal theory of G is contained in the universal theory of H (see [9]). Also, note that any finite sub-structure of Γ(H,X) can eventually be seen in Γ(G,Xn); it follow”
- Hall’s Theorem for Limit Groups (2006, methodology): “Another proof using dierent techniques is given in [ 4 ].”
- Subgroups of direct products of limit groups (2007, unknown): “Limit groups.”
- Limit groups for relatively hyperbolic groups. I. The basic tools (2004, background): “The results of [9] now imply the following result.”
- The Borel Conjecture for hyperbolic and CAT(0)-groups (2009, background): “Expositions about limit groups are for instance [19] and [48].”
- Jsj Decompositions of Groups (2016, unknown): “oincides with M(h 0),soAˆM(A) = M(h 0) = M(H). OneeasilychecksthatanysubgroupofaK-CSAgroupisstillK-CSA.Thisisinfact aconsequenceofthefollowingpropositionsayingthatK-CSAisauniversalproperty. We referto[CG05]forthetopologicalspaceofmarkedgroups,anditsrelationwithuniversal theory. Proposition9.9. Foran”
- The Chabauty space of closed subgroups of the three-dimensional Heisenberg group (2007, background): “In particular, if Fk is the free group on k generators, N(Fk) is the space of marked groups on k generators, which has been the subject of much work since its appearance in the final remarks of [Gromov 1981]; see among others [Grigorchuk 1984; Champetier 2000; Champetier and Guirardel 2005; de Cornu”
- Effective JSJ Decompositions (2004, background): “Champetier and Guirardel gave another characterization of these groups as limits of free groups in a compact space of marked groups [ 14 ].”