Free groups are $L^2$-subgroup rigid
Group Theory
2026-02-05 v2
Abstract
In this paper, we introduce the notion of -subgroup rigid groups and demonstrate that free groups are -subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and -independence for a finitely generated subgroup of a free group, confirming a conjecture by Dicks and Ventura as well as the one by Antolin and Jaikin-Zapirain.
Cite
@article{arxiv.2403.09515,
title = {Free groups are $L^2$-subgroup rigid},
author = {Andrei Jaikin-Zapirain},
journal= {arXiv preprint arXiv:2403.09515},
year = {2026}
}
Comments
Several improvements to the exposition