Geometry & Topology 3 (1999) 405–466

DOI: 10.2140/gt.1999.3.405

arXiv: math.GT/9912248

Abstract

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