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

Volume 238 / 2017

Susumu Hirose, Ryoma Kobayashi Fundamenta Mathematicae 238 (2017), 29-51 MSC: Primary 57M05; Secondary 57M07, 20F38. DOI: 10.4064/fm288-7-2016 Published online: 27 January 2017


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.


  • Susumu HiroseDepartment of Mathematics
    Faculty of Science and Technology
    Tokyo University of Science
    Noda, Chiba, 278-8510, Japan
  • Ryoma KobayashiDepartment of General Education
    Ishikawa National College of Technology
    Tsubata, Ishikawa, 929-0392, Japan

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