An elementary approach to the mapping class group of a surface

We consider an oriented surface $S$ and a cellular complex $X$ of curves on $S$ , defined by Hatcher and Thurston in 1980. We prove by elementary means, without Cerf theory, that the complex $X$ is connected and simply connected. From this we derive an explicit simple presentation of the mapping class group of $S$ , following the ideas of Hatcher–Thurston and Harer.

Keywords

mapping class group, surface, curve complex, group presentation

Mathematical Subject Classification

Primary: 20F05, 20F34, 57M05

Secondary: 20F38, 57M60

References

Forward citations

Publication

Received: 7 January 1999

Revised: 18 November 1999

Accepted: 6 December 1999

Published: 17 December 1999

Proposed: Joan Birman

Seconded: Walter Neumann, Cameron Gordon

Authors

Bronisław Wajnryb
Department of Mathematics Technion 32000 Haifa Israel

Volume 3, issue 1 (1999)

Bronisław Wajnryb