A Presentation of the Mapping Class Groups

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.

Cited by in corpus (6)

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• Mapping class group relations, Stein fillings, and planar open book decompositions
• Signatures of surface bundles and stable commutator lengths of Dehn twists
• Finite presentations of centrally extended mapping class groups