The twist subgroup of the mapping class group of a nonorientable surface

Abstract

Let $\mathcal{T}(N)$ be the subgroup of the mapping class group of a nonorientable surface $N$ (possibly with punctures and/or boundary components) generated by twists about two-sided circles. We obtain a simple generating set for $\mathcal{T}(N)$. As an application we compute the first homology group (abelianization) of $\mathcal{T}(N)$.