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

Micha\l\ Stukow
대한수학회 (The Korean Mathematical Society)|2016.03|대한수학회보 (Bulletin of the KMS)|제53권 제2호|pp. 601-614

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presentationnonorientable surfacemapping class grouptwist subgroup
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초록

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.

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.

참고문헌 (16)

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