Mathematical Research Letters

Volume 4 (1997)

Number 5

A presentation of the mapping of class groups

Pages: 735 – 739



Feng Luo (Department of Mathematics, Rutgers University, New Brunswick, New Jersey)


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.

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