A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists

TL;DR

This paper identifies a minimal generating set for the twist subgroup of the mapping class group of a non-orientable surface using Dehn twists, nearly matching the theoretical lower bound.

Contribution

It provides a small generating set for the twist subgroup of the mapping class group of a non-orientable surface, improving understanding of its algebraic structure.

Findings

The generating set size is just one more than the lower bound.

The lower bound is derived from Hirose’s argument.

The result simplifies the presentation of the twist subgroup.

Abstract

We give a small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists. The difference between the number of the generators and a lower bound of numbers of generators for the twist subgroup by Dehn twists is one. The lower bounds is obtained from an argument of Hirose [5].