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Small Sets of Generators for Handlebody Groups
Abstract
Wajnryb gave a finite presentation of the handlebody group ℳ(Vg) and showed that it is generated by five elements for g≥ 2. Using his relations, we show that ℳ(Vg) is generated by three elements if g≥ 2.
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BibTeX
@misc{altunoz2026small,
title = {{Small Sets of Generators for Handlebody Groups}},
author = {Tülin Altunöz and Celal Can Bellek and Emir Gül and Mehmetcik Pamuk and Oğuz Yıldız},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.01003},
eprint = {2607.01003},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.01003},
}
RIS
TY - UNPB
TI - Small Sets of Generators for Handlebody Groups
AU - Tülin Altunöz
AU - Celal Can Bellek
AU - Emir Gül
AU - Mehmetcik Pamuk
AU - Oğuz Yıldız
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2607.01003
UR - https://arxiv.org/abs/2607.01003
AB - Wajnryb gave a finite presentation of the handlebody group ℳ(V_g) and showed that it is generated by five elements for g≥ 2. Using his relations, we show that ℳ(V_g) is generated by three elements if g≥ 2.
ER -