The rank of actions on -trees
Damien Gaboriau, Gilbert Levitt (1995)
Annales scientifiques de l'École Normale Supérieure
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Displaying similar documents to “Actions of finitely generated groups on -trees”
The rank of actions on -trees
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R-trees and the Bieri-Neumann-Strebel invariant.
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Let G be a finitely generated group. We give a new characterization of its Bieri-Neumann-Strebel invariant Σ(G), in terms of geometric abelian actions on R-trees. We provide a proof of Brown's characterization of Σ(G) by exceptional abelian actions of G, using geometric methods.
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A survey of splitting theorems for abstract groups and their applications. Topics covered include preliminaries, early results, Bass-Serre theory, the structure of G-trees, Serre's applications to SL and length functions. Stallings' theorem, results about accessibility and bounds for splittability. Duality groups and pairs; results of Eckmann and collaborators on PD groups. Relative ends, the JSJ theorems and the splitting results of Kropholler and Roller on PD groups. Notions of quasi-isometry,...