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Boundaries and hierarchically hyperbolic spaces
Mousley, Sarah C.
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https://hdl.handle.net/2142/104790
Description
- Title
- Boundaries and hierarchically hyperbolic spaces
- Author(s)
- Mousley, Sarah C.
- Issue Date
- 2019-04-10
- 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
- Date of Ingest
- 2019-08-23T19:51:43Z
- 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.
- Graduation Semester
- 2019-05
- Type of Resource
- text
- Permalink
- http://hdl.handle.net/2142/104790
- Copyright and License Information
- Copyright 2019 Sarah Camille Mousley Mackay
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Graduate Dissertations and Theses at Illinois PRIMARY
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