# A FINITE PRESENTATION FOR THE TWIST SUBGROUP OF THE MAPPING CLASS GROUP OF A NONORIENTABLE SURFACE

• Stukow, Michal (Institute of Mathematics, University of Gdansk)
• Published : 2016.03.31
• 80 10

#### Abstract

Let $N_{g,s}$ denote the nonorientable surface of genus g with s boundary components. Recently Paris and Szepietowski [12] obtained an explicit finite presentation for the mapping class group $\mathcal{M}(N_{g,s})$ 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 $\mathcal{T}(N_{g,s})$ of $\mathcal{M}(N_{g,s})$ generated by Dehn twists.

#### Keywords

mapping class group;nonorientable surface;twist subgroup;presentation

#### Acknowledgement

Supported by : NCN

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