Geometric Properties of Outer Automorphism Groups of Free Groups
Author | : Samuel Joseph Taylor |
Publisher | : |
Total Pages | : 220 |
Release | : 2014 |
ISBN-10 | : OCLC:882498103 |
ISBN-13 | : |
Rating | : 4/5 (03 Downloads) |
Book excerpt: 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).