2013/09/08 by Pierre Guillot, Guillot, Pierre · 2 citations
Mathematics · Medicine · #History and Theory of Mathematics #Mathematics and Applications #Medical and Biological Sciences
paper · pdf · doi:10.48550/arxiv.1309.1968
We give an account of the theory of dessins d'enfants which is both\nelementary and self-contained. We describe the equivalence of many categories\n(graphs embedded nicely on surfaces, finite sets with certain permutations,\ncertain field extensions, and some classes of algebraic curves), some of which\nare naturally endowed with an action of the absolute Galois group of the\nrational field. We prove that the action is faithful. Eventually we prove that\nthis absolute Galois group embeds into the Grothendieck-Teichm "uller group\nGT0 introduced by Drinfel'd. There are explicit approximations of GT0 by\nfinite groups, and we hope to encourage computations in this area.\n Our treatment includes a result which has not appeared in the literature yet:\nthe Galois action on the subset of regular dessins - that is, those exhibiting\nmaximal symmetry -- is also faithful.\n