Quantifying separability in RAAGs via representations
Group Theory
2025-01-22 v2 Geometric Topology
Abstract
We answer the question asked by Louder, McReynolds and Patel, and prove the following statement. Let L be a RAAG, H a word quasiconvex subgroup of L, then there is a finite dimensional representation of L that separates the subgroup H in the induced Zariski topology. As a corollary, we establish a polynomial upper bound on the size of the quotients used to separate H in L. This implies the same statement for a virtually special group L and, in particular, a fundamental groups of a hyperbolic 3-manifold.
Cite
@article{arxiv.2403.17964,
title = {Quantifying separability in RAAGs via representations},
author = {Olga Kharlampovich and Alina Vdovina},
journal= {arXiv preprint arXiv:2403.17964},
year = {2025}
}
Comments
This is a revised version after the paper has been refereed; arXiv admin note: substantial text overlap with arXiv:2303.03644