Dissertations, Theses, and Capstone Projects
Date of Degree
6-2023
Document Type
Dissertation
Degree Name
Ph.D.
Program
Mathematics
Advisor
Olga Kharlampovich
Committee Members
Ilya Kapovich
Vladimir Shpilrain
Subject Categories
Algebra | Geometry and Topology | Mathematics
Keywords
retractions, fully residually free, elevations, precovers, GICE, ICE
Abstract
We show that for any finitely generated non-abelian subgroup H of a limit group L, there exists a finite-index subgroup K which is fully residually H. This generalizes the result of Wilton that limit groups admit local retractions. We also show that for any finitely generated subgroup of a limit group, there is a finite-dimensional representation of the limit group which separates the subgroup in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate a finitely generated subgroup in a limit group. This generalizes results of Louder, McReynolds, and Patel for free and surface groups.
Recommended Citation
Brown, Keino, "Quantifying Separability in Limit Groups" (2023). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/5338