On squares of Dehn twists about non-separating curves of a non-orientable closed surface
| Autor: | Imoto, Nao, Kobayashi, Ryoma |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The level $2$ mapping class group of an orientable closed surface can be generated by squares of Dehn twists about non-separating curves. On the other hand, the level $2$ mapping class group $\mathcal{M}_2(N_g)$ of a non-orientable closed surface $N_g$ can not be generated by only Dehn twists, and so it can not be generated by squares of Dehn twists about non-separating curves. In this paper, we prove that the Dehn twist subgroup of $\mathcal{M}_2(N_g)$ can not be generated by squares of Dehn twists about non-separating curves either. As an application, we give a finite generating set for the subgroup of $\mathcal{M}_2(N_g)$ generated by Dehn twist about separating curves and squares of Dehn twists about non-separating curves. Moreover, we examine about actions on non-separating simple closed curves of $N_g$ by $\mathcal{M}_2(N_g)$. Comment: 16 pages, 10 figures |
| Databáze: | arXiv |
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