An infinite presentation for the twist subgroup of the mapping class group of a compact non-orientable surface

TL;DR

This paper provides an infinite presentation for the twist subgroup of the mapping class group of a compact non-orientable surface, extending previous finite presentations by utilizing Birman exact sequences.

Contribution

It introduces an infinite presentation for the twist subgroup, building on Stukow's finite presentation and Birman exact sequences, offering a new perspective on the group's structure.

Findings

Infinite presentation for the twist subgroup established

Utilizes Birman exact sequences for derivation

Extends finite presentations to infinite cases

Abstract

A finite presentation for the subgroup of the mapping class group of a compact non-orientable surface generated by all Dehn twists was given by Stukow. In this paper, we give an infinite presentation for this group, mainly using the presentation given by Stukow and Birman exact sequences on mapping class groups of non-orientable surfaces.