Abstract
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.
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Wajnryb, B. A simple presentation for the mapping class group of an orientable surface. Israel J. Math. 45, 157–174 (1983). https://doi.org/10.1007/BF02774014
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DOI: https://doi.org/10.1007/BF02774014