Boundaries and hierarchically hyperbolic spaces

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.

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

2019

Author dc:creator

• Mousley, Sarah C.

Contributors dc:contributor

• Leininger, Christopher J.
• Dunfield, Nathan
• Kapovich, Ilya
• Schupp, Paul

• Teichmuller space
• mapping class group
• right-angled Artin group
• hierarchically hyperbolic
• limit set

Statement dc:rights

• Copyright 2019 Sarah Camille Mousley Mackay

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/104790

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/104790