MINIMAL GROUP-ACTIONS ON LAMBDA-TREES

We consider the existence and uniqueness of minimal invariant subtrees for abelian actions of groups on Lambda-trees, and whether or not a m inimal action is determined up to isomorphism by the hyperbolic length function. The main emphasis is on actions of end type. For a trivial action of end type, there is no minimal invariant subtree. However, if a finitely generated group has an action of end type, the action is n ontrivial and there is a unique minimal invariant subtree. There are e xamples of infinitely generated groups with a nontrivial action of end type for which there is no minimal invariant subtree. These results c an be used to study actions of cut type.