2010/02/16 by Patrick Reynolds, Reynolds, Patrick
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1002.3141
12 pages. reorganized introduction, corrected typos
arxiv created 2010/05/25 · arxiv updated 2010/05/27
Let T be an ℝ-tree, equipped with a very small action of the rank n free group Fn, and let H ≤ Fn be finitely generated. We consider the case where the action Fn \curvearrowright T is indecomposable--this is a strong mixing property introduced by Guirardel. In this case, we show that the action of H on its minimal invarinat subtree TH has dense orbits if and only if H is finite index in Fn. There is an interesting application to dual algebraic laminations; we show that for T free and indecomposable and for H ≤ Fn finitely generated, H carries a leaf of the dual lamination of T if and only if H is finite index in Fn. This generalizes a result of Bestvina-Feighn-Handel regarding stable trees of fully irreducible automorphisms.