Vincent Guirardel - Measure equivalence rigidity for Out(Fn) and dynamical decomposition
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2021-09-06

Measure equivalence is a measurable analogue of quasi-isometry. For instance, two lattices (co-compact or not) in a same Lie group are measurably equivalent by definition. We prove that for N bigger or equal than 3, any countable group that is measure equivalent to Out(Fn)  is virtually isomorphic to it. I will discuss some of the tools introduced for this proof, and in particular, a notion of a canonical dynamic decomposition associated to a subgroup of  which somehow generalizes the dynamical decomposition of a surface associated to a subgroup of Out(Fn) the mapping class group.
This is a joint work with Camille Horbez.