Spaces of left-preorders on free products
Group Theory
2025-07-18 v1
Abstract
Using dynamical techniques we show that there are no isolated elements on the space of left-preorders on a free product of two groups. As a consequence, when the groups are finitely generated, this space is either empty or a Cantor set. For any subgroup of a free product having finite Kurosh rank, we develop similar results for the subspace consisting on the set of left-preorders relative to that subgroup. We provide a generating set for a certain intersection of subgroups of a free product.
Cite
@article{arxiv.2507.12676,
title = {Spaces of left-preorders on free products},
author = {Iván Chércoles Cuesta},
journal= {arXiv preprint arXiv:2507.12676},
year = {2025}
}
Comments
27 pages