= Lickorish-Dehn theorem
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= Dehn-Lickorish theorem
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{synonym}
The <mapping class group> of a compact connected oriented <topological surface>, for orientation-preserving maps fixing its boundary pointwise and isotopies relative to that boundary, is generated by <Dehn twists> about simple closed curves. Boundary-parallel twists are allowed. For a closed surface of positive genus a finite generating collection exists. Permuting boundary components requires additional generators if that larger group is used.
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