Ping-pong and Outer space

Details Ping-pong and Outer space Ping-pong and Outer space

2009-02-24

arxiv.org/abs/0902.4017v4

Journal of Topology and Analysis 2 (2010), no. 2, pp. 173-201

Mathematics

Group Theory

revised version incorporating the referee's suggestions

Scientific paper

10.1142/S1793525310000318

We prove that if $\phi,\psi\in Out(F_N)$ are hyperbolic iwips (irreducible with irreducible powers) such that $<\phi,\psi>\le Out(F_N)$ is not virtually cyclic then some high powers of $\phi$ and $\psi$ 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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