An elementary approach to the mapping class group of a surface

Details An elementary approach to the mapping class group of a surface An elementary approach to the mapping class group of a surface

1999-12-17

arxiv.org/abs/math/9912248v1

Geom. Topol. 3 (1999), 405-466

Mathematics

Geometric Topology

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

Scientific paper

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.

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