Polynomial growth and subgroups of Out(F N )
Annales Henri Lebesgue, Volume 6 (2023), pp. 595-625.


Keywords Nonabelian free groups, outer automorphism groups, space of currents, group actions on trees


This paper, which is the last of a series of three papers, studies dynamical properties of elements of Out(F N ), the outer automorphism group of a nonabelian free group F N . We prove that, for every subgroup H of Out(F N ), there exists an element ϕH such that, for every element g of F N , the conjugacy class [g] has polynomial growth under iteration of ϕ if and only if [g] has polynomial growth under iteration of every element of H.


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