2026-09-21T02:52:56Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/120373 2023-09-05 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Leininger, Christopher Dunfield, Nathan Hirani, Anil Sadanand, Chandrika 2023-05 application/pdf en text Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01 The student, Marissa Chesser, accepted the attached license on 2023-04-14 at 14:00. The student, Marissa Chesser, submitted this Dissertation for approval on 2023-04-14 at 14:05. This Dissertation was approved for publication on 2023-04-16 at 14:19. DSpace SAF Submission Ingestion Package generated from Vireo submission #18989 on 2023-09-01 at 17:13:31 Stable subgroups of handlebody groups Chesser, Marissa 2023-04-16 Geometric Group Theory 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. Thesis eng https://hdl.handle.net/2142/120373 Copyright 2023 Marissa Chesser Ph.D. Dissertation Mathematics University of Illinois at Urbana-Champaign Mathematics