Presentations for the punctured mapping class groups in terms of Artin groups
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 orientationpreserving 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 1999
 arXiv:
 arXiv:math/9911063
 Bibcode:
 1999math.....11063L
 Keywords:

 Mathematics  Geometric Topology;
 57N05;
 20F36;
 20F38
 EPrint:
 Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt15.abs.html