Zariski Closures and Subgroup Separability
Group Theory
2018-11-14 v2 Geometric Topology
Abstract
The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that 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 free or surface group.
Cite
@article{arxiv.1510.04144,
title = {Zariski Closures and Subgroup Separability},
author = {Larsen Louder and D. B. McReynolds and Priyam Patel},
journal= {arXiv preprint arXiv:1510.04144},
year = {2018}
}
Comments
Final version. To appear in Selecta Math