Date of Degree
Algebra | Geometry and Topology | Mathematics
retractions, fully residually free, elevations, precovers, GICE, ICE
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.
Brown, Keino, "Quantifying Separability in Limit Groups" (2023). CUNY Academic Works.
This work is embargoed and will be available for download on Saturday, December 02, 2023
Graduate Center users:
To read this work, log in to your GC ILL account and place a thesis request.
See the GC’s lending policies to learn more.