The Twist Subgroup is generated by two elements

Tulin Altunoz; Mehmetcik Pamuk; Oguz Yildiz

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arXiv · 2103.10483

The Twist Subgroup is generated by two elements

Tulin Altunoz·Mehmetcik Pamuk·Oguz Yildiz

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Abstract

We show that the twist subgroup $\mathcal{T}_g$ of a nonorientable surface of genus $g$ can be generated by two elements for every odd $g\geq27$ and even $g\geq42$. Using these generators, we can also show that $\mathcal{T}_g$ can be generated by two or three commutators depending on $g$ modulo $4$. Moreover, we show that $\mathcal{T}_g$ can be generated by three elements if $g\geq 8$. For this general case, the number of commutator generators is either three or four depending on $g$ modulo $4$ again.

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Tulin Altunoz, Mehmetcik Pamuk, Oguz Yildiz. 2021-03-18. The Twist Subgroup is generated by two elements. https://arxiv.org/abs/2103.10483

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