Volume 1, issue 1 (2001)

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Presentations for the punctured mapping class groups in terms of Artin groups

Catherine Labruere and Luis Paris

Algebraic & Geometric Topology 1 (2001) 73–114
 arXiv: math.GT/9911063
Abstract

Consider an oriented compact surface $F$ of positive genus, possibly with boundary, and a finite set $\mathsc{P}$ of punctures in the interior of $F$, and define the punctured mapping class group of $F$ relatively to $\mathsc{P}$ to be the group of isotopy classes of orientation-preserving homeomorphisms $h:F\to F$ which pointwise fix the boundary of $F$ and such that $h\left(\mathsc{P}\right)=\mathsc{P}$. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic with quotients of Artin groups by some relations involving fundamental elements of parabolic subgroups.

Keywords
Artin groups, presentations, mapping class groups
Mathematical Subject Classification 2000
Primary: 57N05
Secondary: 20F36, 20F38