English

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}
}