Director of Research (if dissertation) or Advisor (if thesis)
Leininger, Christopher J.
Doctoral Committee Chair(s)
Dunfield, Nathan
Committee Member(s)
Kapovich, Ilya
Schupp, Paul
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Teichmuller space
mapping class group
right-angled Artin group
hierarchically hyperbolic
limit set
Abstract
Although the hierarchically hyperbolic space boundary is a generalization of the Gromov boundary, we will show there are fundamental differences between the two. First, we provide negative answers to questions posed by Durham, Hagen, and Sisto on the existence of boundary maps for some hierarchically hyperbolic spaces, namely maps from right-angled Artin groups to mapping class groups. We then answer another question of Durham, Hagen, and Sisto, proving that a Teichmuller geodesic ray does not necessarily converge to a unique point in the hierarchically hyperbolic space boundary of Teichmuller space. In fact, we prove that the limit set can be almost anything allowed by the topology.
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