论文标题
通过互动生成不可定向刺破表面的映射类组
Generating the mapping class group of a non-orientable punctured surface by involutions
论文作者
论文摘要
令$ n_ {g，n} $用$ n $ dumctures表示封闭的$ g $的封闭的非定向表面，让$ {\ Mathcal n} _ {g，n} $表示$ n_ {g，n} $的映射类组。 Szepietowski表明$ {\ Mathcal n} _ {g，n} $由有限的许多互动生成。他的生成集中的元素数量在$ g $和$ n $上线性取决于。在$ n = 0 $的情况下，szepietowski发现了一种与$ g $不取决于$ g $的方式生成的互动生成，这表明$ {\ Mathcal n} _ {g，0} $是通过四个参与而生成的。在本论文中，对于$ n \ geq 0 $，我们证明$ {\ Mathcal n} _ {g，n} $如果$ g \ geq 13 $是奇怪的，则会通过八个参与而生成，如果$ g \ geq 14 $偶数。
Let $N_{g,n}$ denote the closed non-orientable surface of genus $g$ with $n$ punctures and let ${\mathcal N}_{g,n}$ denote the mapping class group of $N_{g,n}$. Szepietowski showed that ${\mathcal N}_{g,n}$ is generated by finitely many involutions. The number of elements in his generating set depends linearly on $g$ and $n$. In the case of $n=0$, Szepietowski found an involution generating set in such a way that the number of its elements does not depend on $g$, showing that ${\mathcal N}_{g,0}$ is generated by four involutions. In this thesis, for $n \geq 0$, we prove that ${\mathcal N}_{g,n}$ is generated by eight involutions if $g \geq 13$ is odd and by eleven involutions if $g \geq 14$ is even.
