The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable Surfaces

2018/11/12 by Du, Xiaoming
#20F38 #57M20 #57N05 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1811.04883

Abstract

Let N_g be the non-orientable surface with genus g, MCG(N_g) be the mapping class group of N_g, T(N_g) be the index 2 subgroup generated by all Dehn twists of MCG(N_g). We prove that for odd genus, T(N_g) can be generated by three elements of finite orders.

Related

• Generating the mapping class group of a nonorientable surface by three torsions
• Torsion Generators of the Twist Subgroup
• Generating twist subgroup of mapping class group of non-orientable surface by involutions
• A finite generating set for the level 2 twist subgroup of the mapping class group of a closed non-orientable surface
• A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists