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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.

Keywords

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}
}

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27 pages