
TL;DR
This paper proves that under certain conditions, high powers of two hyperbolic iwips in Out(F_N) generate a free subgroup where all nontrivial elements are also hyperbolic iwips, analogous to pseudo-Anosov elements in mapping class groups.
Contribution
It establishes that certain pairs of hyperbolic iwips generate free subgroups with all elements being hyperbolic iwips, extending the analogy with pseudo-Anosov elements.
Findings
High powers of hyperbolic iwips generate free subgroups.
All nontrivial elements in these subgroups are hyperbolic iwips.
The result provides an analog of purely pseudo-Anosov free subgroups.
Abstract
We prove that if are hyperbolic iwips (irreducible with irreducible powers) such that is not virtually cyclic then some high powers of and generate a free subgroup of rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a hyperbolic iwip element of 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 .
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