PreprintCC0arXiv
Hopficity of braided and labeled Thompson groups
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 Fn embeds quasi-isometrically as a subgroup of a Hopfian, boundedly acyclic, acyclic group of type Fn that has no proper finite-index subgroups.
Related
- Isomorphic classification of the coordinate algebras of the two-parameter braided quantum groups SL2.
- Thompson's groups are sofic
- The Robust Thompson's Conjecture for Alternating Groups
- On unifying Jones representations of braid groups and Thompson's group
- Conjugacy problems in higher-dimensional Thompson groups
BibTeX
@misc{zhao2026hopficity,
title = {{Hopficity of braided and labeled Thompson groups}},
author = {Mengfei Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42050},
eprint = {2610.42050},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42050},
note = {CC0},
}
RIS
TY - UNPB
TI - Hopficity of braided and labeled Thompson groups
AU - Mengfei Zhao
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42050
UR - https://arxiv.org/abs/2610.42050
AB - 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.
ER -