Date of Award
August 2023
Degree Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematics
First Advisor
Chris Hruska
Committee Members
Craig Guilbault, Richard Stockbridge, Boris Okun, Jonah Gaster
Abstract
What does a typical quotient of a group look like? Gromov looked at the density model of quotients of free groups. The density parameter $d$ measures the rate of exponential growth of the number of relators compared to the size of the Cayley ball. Using this model, he proved that for $d<1/2$, the typical quotient of a free group is non-elementary hyperbolic. Ollivier extended Gromov's result to show that for $d<1/2$, the typical quotient of many hyperbolic groups is also non-elementary hyperbolic.
Żuk and Kotowski--Kotowski proved that for $d>1/3$, a typical quotient of a free group has Property (T). We show that (in a closely related density model) for $1/3
Recommended Citation
Parija, Prayagdeep, "Random Quotients of Hyperbolic Groups and Property (T)" (2023). Theses and Dissertations. 3316.
https://dc.uwm.edu/etd/3316