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Twisting out fully irreducible automorphisms. (English) Zbl 1206.20047
A theme that has been developed in the last two decades or so is that several notions and results in the setting of surface mapping class groups have an analogue in the setting of automorphisms of free groups. For instance, in the context of automorphisms of free groups, the analogue of a simple closed curve on a surface is a splitting of the free group over a cyclic subgroup. The analogue of a pseudo-Anosov mapping class is called a ‘fully irreducible automorphism’, and it is characterized by the property that no nontrivial power of this automorphism fixes the conjugacy class of a proper factor of the free group.
In the paper under review, the authors present a method for constructing fully irreducible automorphisms, by proving an analogue of the following result of Thurston for surface automorphisms: In a subgroup of the mapping class group of a surface generated by Dehn twists along two filling curves, every element not conjugate to a power of one of the twists is pseudo-Anosov.

MSC:
20F65 Geometric group theory
20E36 Automorphisms of infinite groups
20E05 Free nonabelian groups
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