Limit groups with respect to Thompson's group $F$ and other hereditarily separating groups

Aleksander Ivanov; Roland Zarzycki

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arXiv · 2509.20035

Limit groups with respect to Thompson's group $F$ and other hereditarily separating groups

Aleksander Ivanov·Roland Zarzycki

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Abstract

We prove that a limit group over Thompson's group $F$ cannot be an HNN-extension of $F$ with respect to a finitely generated subgroup. On the other hand we give an example of an $F$-limit group which is a centralized HNN-extenstions of $F$. We also study relatively limit groups with respect to $F$ and some other known groups of homeomorphisms of topological spaces. This paper revises and extends some results of the second author from arXiv:1308.6330.

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Aleksander Ivanov, Roland Zarzycki. 2025-09-24. Limit groups with respect to Thompson's group $F$ and other hereditarily separating groups. https://arxiv.org/abs/2509.20035

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