Polynomial growth and subgroups of Out(F_{\tt n})

2022/04/06 by Guerch, Yassine
#20E05 #20E08 #20E36 #20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2204.02700

Abstract

This paper, which is the last of a series of three papers, studies dynamical properties of elements of Out(F_{\tt n}), the outer automorphism group of a nonabelian free group F_{\tt n}. We prove that, for every subgroup H of Out(F_{\tt n}), there exists an element ϕ∈ H such that, for every element g of F_{\tt 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.

Related

• The conjugacy problem in Out(Fm) when the polynomial restrictions are non-growing
• The conjugacy problem for UPG elements of Out(F_n)
• The Tits alternative for Out(F_n) I: Dynamics of exponentially-growing automorphisms
• The Conjugacy Problem for Out(F₃)
• Normal form and parabolic dynamics for quadratically growing automorphisms of free groups