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

TL;DR

This paper provides an explicit normal generating set for the Torelli group of a compact non-orientable surface with boundary, extending known results from orientable cases to non-orientable surfaces.

Contribution

It introduces a specific normal generating set for the Torelli group of non-orientable surfaces with boundary, for genus g ≥ 4 and b ≥ 1, filling a gap in the understanding of these groups.

Findings

Explicit normal generating set for $ ext{I}(N_g^b)$ provided

Extends Torelli group generation results to non-orientable surfaces with boundary

Applicable for genus g ≥ 4 and boundary components b ≥ 1

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 $g\geq4$ and $b\geq1$.