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

2019/03/25 by Leśniak, Marta · 1 citation
#20F05 #20F38 #57N05 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1903.10285

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≥ 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 M(N_g) and give examples.

Cited by

• Minimal Generation of Mapping Class Groups: A Survey of the Nonorientable Case

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