Generators of the Mapping Class Group of a Nonorientable Punctured Surface

TL;DR

This paper demonstrates that the mapping class group of a nonorientable surface with genus at least 14 and punctures can be generated by a small set of elements, including involutions, simplifying its algebraic structure.

Contribution

It provides explicit minimal generating sets for the mapping class group of nonorientable punctured surfaces, including generators that are involutions.

Findings

Generated by five elements for large genus

Can be generated by six involutions

Simplifies understanding of the group's structure

Abstract

Let $\textrm{Mod}(N_{g, p})$ denote the mapping class group of a nonorientable surface of genus $g$ with $p$ punctures. For $g\geq14$, we show that $\textrm{Mod}(N_{g, p})$ can be generated by five elements or by six involutions.