Commentarii Mathematici Helvetici
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Published online: 1998-03-31
Approximations of stable actions on $ \Bbb {R} $-trees
Vincent Guirardel[1] (1) Université de Rennes 1, Rennes, FranceThis article shows how to approximate a stable action of a finitely presented group on an $ \Bbb {R} $-tree by a simplicial one while keeping control over arc stabilizers. For instance, every small action of a hyperbolic group on an $ \Bbb {R} $-tree can be approximated by a small action of the same group on a simplicial tree. The techniques we use highly rely on Rips's study of stable actions on $ \Bbb {R} $-trees and on the dynamical study of exotic components by D. Gaboriau.
Keywords: Stable action, $ \Bbb {R} $$ -trees, Rips theorem, approximation, splitting, Bass-Serre
Guirardel Vincent: Approximations of stable actions on $ \Bbb {R} $-trees. Comment. Math. Helv. 73 (1998), 89-121. doi: 10.1007/s000140050047