Dynamics of free group automorphisms and a subgroup alternative for out(fn)

This thesis is motivated by a foundational result of Thurston which states that pseudo- Anosov mapping classes act on the compactified Teichmüller space with north-south dynamics. We prove that several analogues of pseudo-Anosov mapping classes in the Out(F_N) setting act on the space of projective geodesic currents with generalized north-south dynamics. As an application of our results, we prove several structural theorems for subgroups of Out(F_N).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Uyanik, Caglar

Contributors dc:contributor

• Leininger, Christopher J.
• Kapovich, Ilya
• Tyson, Jeremy
• Dunfield, Nathan

• Free groups
• Mapping class groups
• Pseudo-Anosov
• Fully irreducible
• Hyperbolic

Statement dc:rights

• Copyright 2017 Caglar Uyanik

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/98133

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/98133