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arXiv · 2507.12676

Spaces of left-preorders on free products

Iván Chércoles Cuesta
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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.

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Iván Chércoles Cuesta. 2025-07-16. Spaces of left-preorders on free products. https://arxiv.org/abs/2507.12676

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