Stable subgroups of handlebody groups

Chesser, Marissa

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

Description

Title

Stable subgroups of handlebody groups

Author(s)

Chesser, Marissa

Issue Date

2023-04-16

Director of Research (if dissertation) or Advisor (if thesis)

Leininger, Christopher

Doctoral Committee Chair(s)

Dunfield, Nathan

Committee Member(s)

• Hirani, Anil
• Sadanand, Chandrika

Department of Study

Mathematics

Discipline

Mathematics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• geometric group theory
• handlebody groups

Abstract

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.

Graduation Semester

2023-05

Type of Resource

Thesis

Handle URL

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

Copyright and License Information

Copyright 2023 Marissa Chesser

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