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

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 $h : F \to F$ 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

Mathematical Subject Classification 2000

Primary: 57N05

Secondary: 20F36, 20F38

References

Forward citations

Publication

Received: 6 February 2001

Accepted: 12 February 2001

Published: 24 February 2001

Authors

Catherine Labruere
Laboratoire de Topologie UMR 5584 du CNRS Université de Bourgogne BP 47870 21078 Dijon Cedex France

Luis Paris
Laboratoire de Topologie UMR 5584 du CNRS Université de Bourgogne BP 47870 21078 Dijon Cedex France

Volume 1, issue 1 (2001)

Catherine Labruere and Luis Paris