Polynomial growth and subgroups of $\mathrm{Out}(F_{N})$

Guerch, Yassine

doi:10.5802/ahl.173

Guerch, Yassine

Polynomial growth and subgroups of

Out (F_{N})

Annales Henri Lebesgue, Volume 6 (2023), pp. 595-625.

Metadata

DOI10.5802/ahl.173

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

Abstract

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 $ϕ \in H$ 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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$Polynomial growth and subgroups of <span class="mathjax-formula" data-tex="$\mathrm{Out}(F_{N})$"><math xmlns="http://www.w3.org/1998/Math/MathML" ><mrow><mi mathvariant="normal">Out</mi><mo>(</mo><msub><mi>F</mi> <mi>N</mi> </msub><mo>)</mo></mrow></math></span> - Annales Henri Lebesgue$

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