Geometry & Topology, Vol. 3 (1999) Paper no. 17, pages 405--466.

An elementary approach to the mapping class group of a surface

Bronislaw Wajnryb

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

AMS subject classification. Primary: 20F05,20F34,57M05. Secondary: 20F38,57M60.

DOI: 10.2140/gt.1999.3.405

E-print: arXiv:math.GT/9912248

Submitted to GT on 7 January 1999. (Revised 18 November 1999.) Paper accepted 6 December 1999. Paper published 17 December 1999.

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Bronislaw Wajnryb
Department of Mathematics
Technion, 32000 Haifa, Israel

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