Torsion Elements in the Mapping Class Group of a Surface

Abstract

Given a finite set of $r$ points in a closed surface of genus $g$, we consider the torsion elements in the mapping class group of the surface leaving the finite set invariant. We show that the torsion elements generate the mapping class group if and only if $(g,r)\ne (2,5k+4)$ for some integer $k$.

14 pages, 6 figures

References in corpus (2)

• A finite presentation of the mapping class group of an oriented surface
• A Presentation of the Mapping Class Groups

Cited by in corpus (8)

• Generating Mapping Class Groups by Involutions
• Problems, Questions, and Conjectures about Mapping Class Groups
• Self-similar surfaces: involutions and perfection
• Generating mapping class group by two torsion elements
• Generating the mapping class group by three involutions
• Generating the Extended Mapping Class Group by Three Involutions
• Every mapping class group is generated by 6 involutions
• Generating the mapping class groups by torsions