PreprintCC BY-NC-SA 4.0HAL
ℤ2-free subgroups of Thompson's T are virtually free
Abstract
It is an open problem to determine whether surface groups can embed in Thompson's group V. We prove that any finitely generated subgroup of Thompson's group T without abelian groups of arbitrary high rank is either virtually abelian or virtually free. In particular, surface groups don't embed in T, answering a question of Belk and Moore.
Related
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BibTeX
@misc{bon2026ℤ2free,
title = {{$\mathbbZ^2$-free subgroups of Thompson's $T$ are virtually free}},
author = {Nicolás Matte Bon and Michele Triestino},
howpublished = {HAL},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.16530},
url = {https://hal.science/hal-05852238v1},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - ℤ^2-free subgroups of Thompson's T are virtually free
AU - Nicolás Matte Bon
AU - Michele Triestino
PY - 2026
DA - 2026/11/04
PB - HAL
DO - 10.48550/arxiv.2608.16530
UR - https://hal.science/hal-05852238v1
AB - It is an open problem to determine whether surface groups can embed in Thompson's group V. We prove that any finitely generated subgroup of Thompson's group T without abelian groups of arbitrary high rank is either virtually abelian or virtually free. In particular, surface groups don't embed in T, answering a question of Belk and Moore.
ER -