Generating the mapping class group of a nonorientable surface by three torsions

2020/07/03 by Leśniak, Marta, Szepietowski, Błażej · 1 citation
#20F05 #20F38 #57N05 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2007.01640

Abstract

We prove that the mapping class group M(N_g) of a closed nonorientable surface of genus g different than 4 is generated by three torsion elements. Moreover, for every even integer k≥ 12 and g of the form g=pk+2q(k-1) or g=pk+2q(k-1)+1, where p,q are non-negative integers and p is odd, M(N_g) is generated by three conjugate elements of order k. Analogous results are proved for the subgroup of M(N_g) generated by Dehn twists.

Cited by

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

Related

• The Torsion Generating Set Of The Dehn Twist Subgroups Of Non-orientable Surfaces
• Generating the mapping class group by torsion elements of small order
• Torsion Generators of the Twist Subgroup
• On the Torsion Generators of the Mapping Class Groups
• Generating mapping class group by two torsion elements