Generating mapping class groups of nonorientable surfaces with boundary

TL;DR

This paper provides simple generating sets and computes the abelianizations for mapping class groups of nonorientable surfaces with punctures or boundary, advancing understanding of their algebraic structure.

Contribution

It introduces new simple generating sets for these groups and calculates their abelianizations, which were previously unknown.

Findings

Generated explicit simple sets for mapping class groups.

Computed abelianizations of these groups.

Enhanced understanding of algebraic properties of nonorientable surface groups.

Abstract

We obtain simple generating sets for various mapping class groups of a nonorientable surface with punctures and/or boundary. We also compute the abelianizations of these mapping class groups.