We prove that if T is an $\mathbf R$-tree equipped with a minimal free isometric action of $F_N$ then the $Out(F_N)$-stabilizer of the projective class [T] of [T] is virtually cyclic. As an application, we obtain a new proof of the Tits Alternative for "dynamically large" subgroups of $Out(F_N)$. The talk is based on joint work with Martin Lustig.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/3444
[3] https://www.mpim-bonn.mpg.de/node/249