A presentation of the mapping class groups

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Abstract

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.

Original languageEnglish (US)
Pages (from-to)735-739
Number of pages5
JournalMathematical Research Letters
Volume4
Issue number5
DOIs
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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