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). / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/24948 |
| Date | 01 July 2014 |
| Creators | Taylor, Samuel Joseph |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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