PreprintarXiv licencearXiv
The Involution Rank of MCG(Σ3) Is Four
Abstract
For the closed orientable surface Σ3, we prove irankMCG(Σ3)=4. Thus MCG(Σ3) can be generated by four involutions, but not by three. This settles the genus-three case of Farb's problem on generation by involutions.
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BibTeX
@misc{guo2026involution,
title = {{The Involution Rank of $\MCG(Σ_3)$ Is Four}},
author = {Qilong Guo and Dongqi Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22774},
eprint = {2610.22774},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22774},
}
RIS
TY - UNPB
TI - The Involution Rank of MCG(Σ_3) Is Four
AU - Qilong Guo
AU - Dongqi Sun
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.22774
UR - https://arxiv.org/abs/2610.22774
AB - For the closed orientable surface Σ_3, we prove irankMCG(Σ_3)=4. Thus MCG(Σ_3) can be generated by four involutions, but not by three. This settles the genus-three case of Farb's problem on generation by involutions.
ER -