Groups acting on trees: From local to global structure
نویسندگان
چکیده
منابع مشابه
Superstable groups acting on trees
We study superstable groups acting on trees. We prove that an action of an ω-stable group on a simplicial tree is trivial. This shows that an HNN-extension or a nontrivial free product with amalgamation is not ωstable. It is also shown that if G is a superstable group acting nontrivially on a Λ-tree, where Λ = Z or Λ = R, and if G is either α-connected and Λ = Z, or if the action is irreducible...
متن کاملON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS
Abstract. In this paper we show that if G is a group acting on a tree X with inversions and if (T Y ) is a fundamental domain for the action of G on X, then there exist a group &tildeG and a tree &tildeX induced by (T Y ) such that &tildeG acts on &tildeX with inversions, G is isomorphic to &tilde G, and X is isomorphic to &tildeX. The pair (&tilde G &tildeX) is called the quasi universal cover...
متن کاملA condition that prevents groups from acting nontrivially on trees
An R–tree is a geodesic metric space in which there is a unique arc connecting each pair of points. A group Γ is said to have property FR if for every action of Γ by isometries on an R–tree, the fixed point set Fix(Γ) is nonempty. Serre’s property FA is similar except that one considers only actions on simplicial trees. A group has FA if and only if it cannot be expressed as a nontrivial amalga...
متن کاملAmenability of Groups Acting on Trees
This note describes the first example of a group that is amenable, but cannot be obtained by subgroups, quotients, extensions and direct limits from the class of groups locally of subexponential growth. It has a balanced presentation ∆ = 〈b, t| [b, t]b, [[[b, t], b], b]〉. In the proof, I show that ∆ acts transitively on a 3-regular tree, and that Γ = 〈b, b −1 〉 stabilizes a vertex and acts by r...
متن کاملCompletely metrisable groups acting on trees
We consider actions of completely metrisable groups on simplicial trees in the context of the Bass–Serre theory. Our main result characterises continuity of the amplitude function corresponding to a given action. Under fairly mild conditions on a completely metrisable group G, namely, that the set of elements generating a non-discrete or finite subgroup is somewhere dense, we show that in any d...
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ژورنال
عنوان ژورنال: Publications mathématiques de l'IHÉS
سال: 2000
ISSN: 0073-8301,1618-1913
DOI: 10.1007/bf02698915