Mathematical Research Letters
Volume 4 (1997)
A presentation of the mapping of class groups
Pages: 735 – 739
Given a compact orientable surface, the mapping class group is shown to have 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.