%0 Generic %1 Reynolds2010 %A Reynolds, Patrick %D 2010 %K boundary indecomposable outer space trees %T On indecomposable trees in the boundary of Outer space %U http://arxiv.org/abs/1002.3141 %X Let $T$ be an $R$-tree, equipped with a very small action of the rank $n$ free group $F_n$, and let $H F_n$ be finitely generated. We consider the case where the action $F_n T$ 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 $T_H$ has dense orbits if and only if $H$ is finite index in $F_n$. There is an interesting application to dual algebraic laminations; we show that for $T$ free and indecomposable and for $H F_n$ finitely generated, $H$ carries a leaf of the dual lamination of $T$ if and only if $H$ is finite index in $F_n$. This generalizes a result of Bestvina-Feighn-Handel regarding stable trees of fully irreducible automorphisms.

@misc{Reynolds2010, abstract = { Let $T$ be an $\mathbb{R}$-tree, equipped with a very small action of the rank $n$ free group $F_n$, and let $H \leq F_n$ be finitely generated. We consider the case where the action $F_n \curvearrowright T$ 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 $T_H$ has dense orbits if and only if $H$ is finite index in $F_n$. There is an interesting application to dual algebraic laminations; we show that for $T$ free and indecomposable and for $H \leq F_n$ finitely generated, $H$ carries a leaf of the dual lamination of $T$ if and only if $H$ is finite index in $F_n$. This generalizes a result of Bestvina-Feighn-Handel regarding stable trees of fully irreducible automorphisms. }, added-at = {2010-11-01T12:43:06.000+0100}, author = {Reynolds, Patrick}, biburl = {https://www.bibsonomy.org/bibtex/28c0fa51fc4d868bd36b6e44e02dcfab5/uludag}, description = {On indecomposable trees in the boundary of Outer space}, interhash = {bf04f4f8fafb29fac645544a4f57a8a1}, intrahash = {8c0fa51fc4d868bd36b6e44e02dcfab5}, keywords = {boundary indecomposable outer space trees}, note = {cite arxiv:1002.3141 Comment: 12 pages. reorganized introduction, corrected typos}, timestamp = {2010-11-01T12:43:06.000+0100}, title = {On indecomposable trees in the boundary of Outer space}, url = {http://arxiv.org/abs/1002.3141}, year = 2010 }