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.
Notes on file formats
Catherine Labruere and Luis Paris
Laboratoire de Topologie, UMR 5584 du CNRS
Universite de Bourgogne, BP 47870 21078 Dijon Cedex, France
Email: clabruer@u-bourgogne.fr, lparis@u-bourgogne.fr
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