Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(2): 601-614

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.601

Copyright © The Korean Mathematical Society.

A finite presentation for the twist subgroup of the mapping class group of a nonorientable surface

Micha\l\ Stukow

University of Gda\'nsk

Abstract

Let $N_{g,s}$ denote the nonorientable surface of genus $g$ with $s$ boundary components. Recently Paris and Szepietowski \cite{SzepParis} obtained an explicit finite presentation for the mapping class group $\cM(N_{g,s})$ of the surface $N_{g,s}$, where $s\in\{0,1\}$ and $g+s>3$. Following this work, we obtain a finite presentation for the subgroup $\cT(N_{g,s})$ of $\cM(N_{g,s})$ generated by Dehn twists.

Keywords: mapping class group, nonorientable surface, twist subgroup, presentation

MSC numbers: Primary 57N05; Secondary 20F38, 57M99

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