A Presentation of the Mapping Class Groups

1998/01/07 by Feng Luo
Mathematics · #math.GT #msc:57

paper · pdf

published as Mathematical Research Letters, Vol. 4, 1997, 735-739.

arxiv created 1998/01/07 · arxiv updated 2009/11/30

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.

Related

• A finite presentation of the mapping class group of an oriented surface
• Generating the surface mapping class group by two elements
• An infinite presentation for the twist subgroup of the mapping class group of a compact non-orientable surface
• Minimal Generation of Mapping Class Groups: A Survey of the Orientable Case
• A small generating set for the twist subgroup of the mapping class group of a non-orientable surface by Dehn twists