An elementary approach to the mapping class group of a surface

Wajnryb, Bronisław¹

¹ Department of Mathematics, Technion, 32000 Haifa, Israel

Geometry & topology, Tome 3 (1999) no. 1, pp. 405-466.

Résumé

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.

Détail

DOI : 10.2140/gt.1999.3.405

Keywords: mapping class group, surface, curve complex, group presentation

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