QUASI-ACTIONS ON TREES AND PROPERTY (QFA)

We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre’s Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including SL(n, Z) for n 3. We also give a way of thinking about Property (QFA) by breaking it down into statements about particular classes of trees.