A simple presentation for the mapping class group of an orientable surface
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LetF n.k be an orientable compact surface of genusn withk boundary components. For a suitable choice of 2n + 1 simple closed curves onF n,1 the corresponding Dehn twists generate bothM n,o andM n,1. A complete system of relations is determined for these generators and the presentations ofM n,0 andM n,1 obtained in this way are much simpler than the known presentations.
KeywordsBoundary Component Braid Group Mapping Class Group Orientable Surface Simple Move
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