The Twist Subgroup is generated by two elements

2021/03/18 by Altunoz, Tulin, Pamuk, Mehmetcik, Yildiz, Oguz · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2103.10483

Abstract

We show that the twist subgroup T_g of a nonorientable surface of genus g can be generated by two elements for every odd g≥27 and even g≥42. Using these generators, we can also show that T_g can be generated by two or three commutators depending on g modulo 4. Moreover, we show that T_g can be generated by three elements if g≥ 8. For this general case, the number of commutator generators is either three or four depending on g modulo 4 again.

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

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