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

Labruere, Catherine; Paris, Luis

doi:10.2140/agt.2001.1.73

Labruere, Catherine ¹ ; Paris, Luis ¹

¹Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 73-114

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Résumé

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.

DOI : 10.2140/agt.2001.1.73

Keywords: Artin groups, presentations, mapping class groups

Affiliations des auteurs :

Labruere, Catherine ¹ ; Paris, Luis ¹

¹ Laboratoire de Topologie, UMR 5584 du CNRS, Université de Bourgogne, BP 47870, 21078 Dijon Cedex, France

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Labruere, Catherine; Paris, Luis. Presentations for the punctured mapping class groups in terms of Artin groups. Algebraic and Geometric Topology, Tome 1 (2001) no. 1, pp. 73-114. doi: 10.2140/agt.2001.1.73

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