Doctoral thesis
Open access

On Infinite Groups and their Actions: From Group Actions on Graphs to Group Actions on Complexes

Imprimatur date2022-09-01
Defense date2022-08-29

Understanding how a group can act on a given type of space can be a valuable tool for proving properties of both the group and the space. This thesis focuses on three distinct topics involving actions of infinite groups on graphs, cube complexes and metric spaces.

In the first part, we answer a question by Grigorchuk asking whether it is possible to give an explicit and elementary description of a CAT(0) cube complex on which the groups he defined act and, if so, to describe these ac- tions. In the following, we present the results of joint projects with P-H. Leemann where we are interested in the stability of certain properties of groups for the wreath product. Then, we study the stability of these properties for the wreath product in a more general framework. Finally, we study the notion of expansion for objects of dimension greater than 1.

  • Geometric group theory
  • Grigorchuk groups
  • Wreath product
  • Schreier Graphs
  • High dimensional expanders
  • CAT(0) cube complexes
Citation (ISO format)
SCHNEEBERGER, Grégoire. On Infinite Groups and their Actions: From Group Actions on Graphs to Group Actions on Complexes. 2022. doi: 10.13097/archive-ouverte/unige:166747
Main files (2)

Technical informations

Creation02/07/2023 11:27:00 AM
First validation02/07/2023 11:27:00 AM
Update time05/10/2023 11:12:41 AM
Status update05/10/2023 11:12:41 AM
Last indexation09/18/2023 9:43:30 PM
All rights reserved by Archive ouverte UNIGE and the University of GenevaunigeBlack