Torsion normal generators of the mapping class group of a non-orientable surface

Marta Leśniak

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arXiv · 1903.10285

Torsion normal generators of the mapping class group of a non-orientable surface

Marta Leśniak

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Abstract

We show that the normal closure of any periodic element of the mapping class group of a non-orientable surface whose order is greater than 2 contains the commutator subgroup, which for $g\geq 7$ is equal to the twist subgroup, and provide necessary and sufficient conditions for the normal closures of involutions to contain the twist subgroup. Finally, we provide a criterion for a periodic element to normally generate $\mathcal{M}(N_g)$ and give examples.

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Marta Leśniak. 2019-03-25. Torsion normal generators of the mapping class group of a non-orientable surface. https://arxiv.org/abs/1903.10285

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