English

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

Geometric Topology 2023-03-06 v3 Group Theory

Abstract

For a compact surface SS, let I(S)\mathcal{I}(S) denote the Torelli group of SS. For a compact orientable surface Σ\Sigma, I(Σ)\mathcal{I}(\Sigma) is generated by BSCC maps and BP maps. For a non-orientable closed surface NN, I(N)\mathcal{I}(N) is generated by BSCC maps and BP maps. In this paper, we give an explicit normal generating set for I(Ngb)\mathcal{I}(N_g^b), where NgbN_g^b is a genus-gg compact non-orientable surface with bb boundary components for g4g\geq4 and b1b\geq1.

Keywords

Cite

@article{arxiv.1601.06257,
  title  = {A normal generating set for the Torelli group of a compact non-orientable surface},
  author = {Ryoma Kobayashi},
  journal= {arXiv preprint arXiv:1601.06257},
  year   = {2023}
}

Comments

12 pages, 13 figures

R2 v1 2026-06-22T12:35:21.868Z