A normal generating set for the Torelli group of a non-orientable closed surface
Volume 238 / 2017
Fundamenta Mathematicae 238 (2017), 29-51
MSC: Primary 57M05; Secondary 57M07, 20F38.
DOI: 10.4064/fm288-7-2016
Published online: 27 January 2017
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 (see Powell (1978)). We give a normal generating set of $\mathcal {I}(N_g)$ for $g\geq 4$, where $N_g$ is a genus-$g$ non-orientable closed surface.
