论文标题
通过三个扭力生成不可定向表面的映射类组
Generating the mapping class group of a nonorientable surface by three torsions
论文作者
论文摘要
我们证明，映射类组$ \ MATHCAL {M}（N_G）$的封闭式不可方向的表面$ G $不同于4的4个扭转元素。此外，对于$ g = pk+2q（k-1）$或$ g = pk+g = pk+2q（k-1）+1 $的每一个偶数整数$ k \ ge 12 $和$ g $，其中$ p，q $是非阴性整数，$ p $是奇数，$ \ \ \ \ m nathcal {m}（m}（n_g）$由$ k $ kkate $ kkate $ knjate of thred conjate。对于Dehn Twists生成的$ \ Mathcal {M}（N_G）$的子组证明了类似的结果。
We prove that the mapping class group $\mathcal{M}(N_g)$ of a closed nonorientable surface of genus $g$ different than 4 is generated by three torsion elements. Moreover, for every even integer $k\ge 12$ and $g$ of the form $g=pk+2q(k-1)$ or $g=pk+2q(k-1)+1$, where $p,q$ are non-negative integers and $p$ is odd, $\mathcal{M}(N_g)$ is generated by three conjugate elements of order $k$. Analogous results are proved for the subgroup of $\mathcal{M}(N_g)$ generated by Dehn twists.
