Generating the Twist Subgroup by Involutions

TL;DR

This paper investigates the generation of the twist subgroup of the mapping class group for nonorientable surfaces using involutions, providing minimal generating sets and advancing understanding of its algebraic structure.

Contribution

It introduces new minimal involution generating sets for the twist subgroup of nonorientable surface mapping class groups.

Findings

Identified minimal involution generating sets for the twist subgroup

Demonstrated the efficiency of the proposed generating sets

Enhanced understanding of the algebraic structure of the twist subgroup

Abstract

For a nonorientable surface, the twist subgroup is an index 2 subgroup of the mapping class group. It is generated by Dehn twists about two-sided simple closed curves. In this paper, we study involution generators of the twist subgroup. We give generating sets of involutions with the smallest number of elements our methods allow.