University of Illinois Urbana-Champaign

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

Uyanik, Caglar

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

Description

Title
Dynamics of free group automorphisms and a subgroup alternative for out(fn)
Author(s)
Uyanik, Caglar
Issue Date
2017-06-26
Director of Research (if dissertation) or Advisor (if thesis)
  • Leininger, Christopher J.
  • Kapovich, Ilya
Doctoral Committee Chair(s)
Tyson, Jeremy
Committee Member(s)
Dunfield, Nathan
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
  • Free groups
  • Mapping class groups
  • Pseudo-Anosov
  • Fully irreducible
  • Hyperbolic
Abstract
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).
Graduation Semester
2017-08
Type of Resource
text
Permalink
http://hdl.handle.net/2142/98133
Copyright and License Information
Copyright 2017 Caglar Uyanik

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