Stable subgroups of handlebody groups

The main result of this thesis is that a finitely generated subgroup of the genus two handlebody group is stable if and only if the orbit map to the disk graph is a quasi-isometric embedding. To this end, we prove that the genus two handlebody group is a hierarchically hyperbolic group, and that the maximal hyperbolic space in the hierarchy is quasi-isometric to the disk graph of a genus two handlebody by appealing to a construction of Hamenstadt-Hensel. We then utilize the characterization of stable subgroups of hierarchically hyperbolic groups provided by Abbott-Behrstock-Durham. We also present several applications of the main theorems, and show that the higher genus analogues of the genus two results do not hold.

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

2023

Author dc:creator

• Chesser, Marissa

Contributors dc:contributor

• Leininger, Christopher
• Dunfield, Nathan
• Hirani, Anil
• Sadanand, Chandrika

• Geometric Group Theory
• Handlebody Groups

Statement dc:rights

• Copyright 2023 Marissa Chesser

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120373

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120373