A Presentation of the Mapping Class Groups

Details A Presentation of the Mapping Class Groups A Presentation of the Mapping Class Groups

1998-01-07

arxiv.org/abs/math/9801025v1

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

Mathematics

Geometric Topology

Scientific paper

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.

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