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arXiv · 0902.4017

Ping-pong and Outer space

Ilya Kapovich·Martin Lustig
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Abstract

We prove that if $ϕ,ψ\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<ϕ,ψ>\le Out(F_N)$ is not virtually cyclic then some high powers of $ϕ$ and $ψ$ generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of $Out(F_N)$ is strongly analogous to being a pseudo-Anosov element of a mapping class group, so the above result provides analogs of "purely pseudo-Anosov" free subgroups of $Out(F_N)$.

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Ilya Kapovich, Martin Lustig. 2010-02-12. Ping-pong and Outer space. https://doi.org/10.1142/s1793525310000318

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