Surface groups are flexibly stable
Group Theory
2025-01-10 v3 Geometric Topology
Abstract
We show that surface groups are flexibly stable in permutations. This is the first non-trivial example of a non-amenable flexibly stable group. Our method is purely geometric and relies on an analysis of branched covers of hyperbolic surfaces. Along the way we establish a quantitative variant of the LERF property for surface groups which may be of independent interest.
Cite
@article{arxiv.1901.07182,
title = {Surface groups are flexibly stable},
author = {Nir Lazarovich and Arie Levit and Yair Minsky},
journal= {arXiv preprint arXiv:1901.07182},
year = {2025}
}
Comments
published version, with some corrections