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

Catherine Labruere, Luis Paris
2001 Algebraic and Geometric Topology  
Consider an oriented compact surface F of positive genus, possibly with boundary, and a finite set P of punctures in the interior of F, and define the punctured mapping class group of F relatively to P to be the group of isotopy classes of orientation-preserving homeomorphisms h: F-->F which pointwise fix the boundary of F and such that h(P) = P. In this paper, we calculate presentations for all punctured mapping class groups. More precisely, we show that these groups are isomorphic with
more » ... ts of Artin groups by some relations involving fundamental elements of parabolic subgroups.
doi:10.2140/agt.2001.1.73 fatcat:jvxg3bp44bcmlpdxfpc7k2gpu4