A normal generating set for the Torelli group of a compact non-orientable surface

Abstract

For a compact surface $S$, let $\mathcal{I}(S)$ denote the Torelli group of $S$. For a compact orientable surface $\Sigma$, $\mathcal{I}(\Sigma )$ is generated by BSCC maps and BP maps. For a non-orientable closed surface $N$, $\mathcal{I}(N)$ is generated by BSCC maps and BP maps. In this paper, we give an explicit normal generating set for $\mathcal{I}(N_g^b)$, where $N_g^b$ is a genus-$g$ compact non-orientable surface with $b$ boundary components for $g\ge 4$ and $b\ge 1$.

12 pages, 13 figures

References in corpus (2)

• A presentation for the mapping class group of a nonorientable surface
• A normal generating set for the Torelli group of a non-orientable closed surface