论文标题
通过两个扭转元素生成映射类组
Generating mapping class group by two torsion elements
论文作者
论文摘要
我们证明，$ g $的封闭连接的定向表面的映射类组是由$ g \ geq 6 $的两个订单$ g $的要素生成的。此外，对于$ g \ geq 7 $，我们找到了两个要素的生成集，即$ g $和$ g'$，这是$ g $的最小除数，因此$ g'> 2 $。此外，我们证明了它是由$ g/\ gcd（g，k）$的两个元素生成的，$ g \ geq 3k^2+4k+1 $和任何正整数$ k $。
We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by two elements of order $g$ for $g\geq 6$. Moreover, for $g\geq 7$ we found a generating set of two elements, of order $g$ and $g'$ which is the least divisor of $g$ such that $g'>2$. Furthermore, we proved that it is generated by two elements of order $g/\gcd (g,k)$ for $g\geq 3k^2+4k+1$ and any positive integer $k$.
