Algebraic and Geometric Topology 1 (2001), paper no. 5, pages 73-114.

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

Catherine Labruere and Luis Paris

Abstract. 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 quotients of Artin groups by some relations involving fundamental elements of parabolic subgroups.

Keywords. Artin groups, presentations, mapping class groups

AMS subject classification. Primary: 57N05. Secondary: 20F36, 20F38.

DOI: 10.2140/agt.2001.1.73

E-print: arXiv:math.GT/9911063

Submitted: 6 February 2001. Accepted: 12 February 2001. Published: 24 February 2001.

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Catherine Labruere and Luis Paris
Laboratoire de Topologie, UMR 5584 du CNRS
Universite de Bourgogne, BP 47870 21078 Dijon Cedex, France

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