Geometric properties of outer automorphism groups of free groups

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2014-05

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Abstract

This thesis examines geometric aspects of the outer automorphism group of a finitely generate free group. Using recent advances made in understanding mapping class groups as our primary motivation, we refine methods to understand the structure of Out(F_n) via its action on free factors of F_n. Our investigation has a number of applications: First, we give a natural notion of projection between free factors, extending a construction of Bestvina-Feighn. Second, we provide a new method to produce fully irreducible automorphisms of F_n using combinations of automorphism supported on free factors. Finally, we use these results to give a general construction of quasi-isometric embeddings from right-angled Artin groups into Out(F_n).

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