Pseudogroups of isometries of R and Rips' theorem on free actions on R-trees

D. Gaboriau, G. Levitt and F. Paulin

Article publié :

Israel Jour. of Math, 87 (1994) 403-428.

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We give a shorter proof of Rips' theorem saying that a finitely generated group acting freely on an R-tree is a free product of free abelian groups and surface groups. For this, we study the dynamical properties of finite sets of partial isometries of R.