Generating the mapping class group of a nonorientable surface of genus $g \geq 13$ by two elements

TL;DR

This paper proves that for nonorientable surfaces of genus at least 13, the mapping class group can be generated by just two elements, improving previous bounds.

Contribution

It establishes a minimal generating set of size two for the mapping class group of nonorientable surfaces of genus g ≥ 13, lowering the known genus threshold.

Findings

Mapping class group of N_g is generated by two elements for g ≥ 13.

Improves previous genus bound from 19 to 13.

Simplifies understanding of the algebraic structure of these groups.

Abstract

Let $N_g$ be a closed, connected, nonorientable surface of genus $g$. We prove that for $g \ge 13$, the mapping class group $\text{Mod}(N_g)$ can be generated by exactly two elements. This improves the previously known bound of $g \ge 19$.