Some hyperbolic out (Fn)-graphs and nonunique ergodicity of very small Fn-trees

We define a new graph on which Out(FN) acts and show that it is hyperbolic. Also we give a new proof, based on an argument by Bestvina and Fujiwara, that the Free Factor Graph satises Weak Proper Discontinuity (WPD), and show that the Intersection Graph satises WPD as well. Furthermore, in joint work with Patrick Reynolds, we construct nonuniquely ergodic, nongeometric, arational FN-trees.