An elementary approach to the mapping class group of a surface

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.

62 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol3/paper17.abs.html

References in corpus (1)

• A finite presentation of the mapping class group of an oriented surface

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