Generating the mapping class group of a non-orientable punctured surface by involutions

Abstract

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 $n\ge 0$, we prove that ${\mathcal{N}}_{g,n}$ is generated by eight involutions if $g\ge 13$ is odd and by eleven involutions if $g\ge 14$ is even.

arXiv comment16 pages, 21 figures