#### Volume 3, issue 1 (1999)

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An elementary approach to the mapping class group of a surface

### Bronisław Wajnryb

Geometry & Topology 3 (1999) 405–466
 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