Abstract
A Recognition Theorem for Polynomially Growing Outer Automorphisms of the Free Group By Gregory MacLean Schinke Fein Dissertation Director: Professor Mark E. Feighn Feighn and Handel’s recognition theorem for Out(Fn) provides invariants that canonically determine any forward rotationless outer automorphism of the free group. We ask to what extent those invariants can be extended to outer automorphisms with some periodic behavior. Many of the same constructions do not have natural analogs, in particular because of the possible lack of principal representatives in this setting. However, by restricting our attention to polynomial growth outer automorphisms and using train track technology, we are able to find a special set of lines in the free group that encode all the dynamical information of these non-forward rotationless maps.
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