Boundaries and hierarchically hyperbolic spaces

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

Mousley, Sarah C.

关键词: Teichmuller space;    mapping class group;    right-angled Artin group;    hierarchically hyperbolic;    limit set;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/104790/MOUSLEY-DISSERTATION-2019.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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.