A Presentation of the Mapping Class Groups
Geometric Topology
2007-05-23 v1
Abstract
Using the works of Gervais, Harer, Hatcher and Thurston and others, we show that the mapping class group of a compact orientable surface has a presentation so that the generators are the set of all Dehn twists and the relations are supported in subsurfaces homeomorphic to the one-holed torus or the four-holed sphere. It turns out that all the relations were discovered by Dehn in 1938.
Keywords
Cite
@article{arxiv.math/9801025,
title = {A Presentation of the Mapping Class Groups},
author = {Feng Luo},
journal= {arXiv preprint arXiv:math/9801025},
year = {2007}
}