Stabilizers of R-trees with Free Isometric Actions

نویسنده

  • MARTIN LUSTIG
چکیده

We prove that if T is an R-tree with a minimal free isometric action of FN , then the Out(FN )-stabilizer of the projective class [T ] is virtually cyclic. For the special case where T = T+(φ) is the forward limit tree of an atoroidal iwip element φ ∈ Out(FN ) this is a consequence of the results of Bestvina, Feighn and Handel [6], via very different methods. We also derive a new proof of the Tits alternative for subgroups of Out(FN ) containing an iwip (not necessarily atoroidal): we prove that every such subgroup G ≤ Out(FN ) is either virtually cyclic or contains a free subgroup of rank two. The general case of the Tits alternative for subgroups of Out(FN ) is due to Bestvina, Feighn and Handel.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Number of Orbits of Branch Points of 7î-trees

An A-tree is a metric space in which any two points are joined by a unique arc. Every arc is isometric to a closed interval of R . When a group G acts on a tree (Z-tree) X without inversion, then X/G is a graph. One gets a presentation of G from the quotient graph X/G with vertex and edge stabilizers attached. For a general R-tree X, there is no such combinatorial structure on X/G . But we can ...

متن کامل

Geometric Intersection Number and Analogues of the Curve Complex for Free Groups

For the free group FN of finite rank N ≥ 2 we construct a canonical Bonahon-type, continuous and Out(FN )-invariant geometric intersection form 〈 , 〉 : cv(FN ) × Curr(FN ) → R≥0. Here cv(FN ) is the closure of unprojectivized Culler-Vogtmann’s Outer space cv(FN ) in the equivariant Gromov-Hausdorff convergence topology (or, equivalently, in the length function topology). It is known that cv(FN ...

متن کامل

Quasi-actions on trees I. Bounded valence

Given a bounded valence, bushy tree T , we prove that any cobounded quasi-action of a group G on T is quasiconjugate to an action of G on another bounded valence, bushy tree T ′. This theorem has many applications: quasi-isometric rigidity for fundamental groups of finite, bushy graphs of coarse PD(n) groups for each fixed n; a generalization to actions on Cantor sets of Sullivan’s theorem abou...

متن کامل

Deformation and rigidity of simplicial group actions on trees

We study a notion of deformation for simplicial trees with group actions (G{ trees). Here G is a xed, arbitrary group. Two G{trees are related by a deformation if there is a nite sequence of collapse and expansion moves joining them. We show that this relation on the set of G{trees has several characterizations, in terms of dynamics, coarse geometry, and length functions. Next we study the defo...

متن کامل

Closed Groups Induced by Finitary Permutations and Their Actions on Trees

We describe permutation groups G ≤ Sym(ω) such that G is the closure of the subgroup of all elements with finite support and G can be realized as Aut(M) where M is a saturated structure. We also study isometric actions of such groups on real trees.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009