Small torsion generating sets for hyperelliptic mapping class groups

Abstract

We prove that both the hyperelliptic mapping class group and the extended hyperelliptic mapping class group are generated by two torsion elements. We also compute the index of the subgroup of the hyperelliptic mapping class group which is generated by involutions and we prove that the extended hyperelliptic mapping class group is generated by three orientation reversing involutions.

A version of the paper which appeared in Topology and its {A}pp

References in corpus (4)

• Generating Mapping Class Groups by Involutions
• The extended mapping class group is generated by three symmetries
• Conjugacy classes of finite subgroups of certain mapping class groups
• Generating the surface mapping class group by two elements

Cited by in corpus (7)

• Generating mapping class groups of nonorientable surfaces with boundary
• Mapping class groups of covers with boundary and braid group embeddings
• The liftable mapping class group of balanced superelliptic covers
• A Hyperelliptic View on Teichmuller Space. I
• Generating mapping class group by two torsion elements
• Generating the mapping class group by three involutions
• A small generating set for the balanced superelliptic handlebody group