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arXiv · 2610.42050

Hopficity of braided and labeled Thompson groups

Mengfei Zhao
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Abstract

We prove that the braided Thompson groups $BV$ and $BF$ are Hopfian, answering the two parts of Zaremsky's question. We also prove that, for every discrete group $G$, the labeled Thompson group $V(G)$ is Hopfian if and only if $G$ is Hopfian, proving a conjecture of Wu--Wu--Zhao--Zhou. The second result allows us to prove a new embedding result for Hopfian groups: every Hopfian group of type $F_n$ embeds quasi-isometrically as a subgroup of a Hopfian, boundedly acyclic, acyclic group of type $F_n$ that has no proper finite-index subgroups.

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Mengfei Zhao. 2026-10-30. Hopficity of braided and labeled Thompson groups. https://arxiv.org/abs/2610.42050

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