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Galois actions on surfaces and a higher genus Grothendieck-Teichmüller group
We construct a modular operad $\mathbf{S}$ of mapping class groupoids modelling the higher-genus Teichmüller tower, with compositions and contractions encoding surface gluing. We prove a presentation theorem for maps out of $\mathbf{S}$ using genus-zero and genus-one generators and relations. Applyi
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