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

Abstract

For a closed surface $S$, its Torelli group $\mathcal{I}(S)$ is the subgroup of the mapping class group of $S$ consisting of elements acting trivially on $H_1(S;\mathbb{Z})$. When $S$ is orientable, a generating set for $\mathcal{I}(S)$ is known. In this paper, we give a normal generating set of $\mathcal{I}(N_g)$ for $g\ge 4$, where $N_g$ is a genus-$g$ non-orientable closed surface.

arXiv comment23 pages, 27 figures

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Cited by in corpus (2)

• A finite presentation of the level $2$ principal congruence subgroup of $GL(n;\mathbb{Z})$
• A normal generating set for the Torelli group of a compact non-orientable surface