Displaying similar documents to “Actions of finitely generated groups on -trees”

R-trees and the Bieri-Neumann-Strebel invariant.

Gilbert Levitt (1994)

Publicacions Matemàtiques


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.

The geometry of abstract groups and their splittings.

Charles Terence Clegg Wall (2003)

Revista Matemática Complutense


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,...