Publications of the Research Institute for Mathematical Sciences
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Published online: 2006-09-30
Belyi-Extending Maps and the Galois Action on Dessins d’EnfantsMelanie Matchett Wood (1) Princeton University, USA
We study the absolute Galois group by looking for invariants and orbits of its faithful action on Grothendieck’s dessins d’enfants. We deﬁne a class of functions called Belyi-extending maps, which we use to construct new Galois invariants of dessins from previously known invariants. Belyi-extending maps are the source of “new-type” relations on the injection of the absolute Galois group into the Grothendieck–Teichmüller group. We make explicit how to get from a general Belyi-extending map to formula for its associated invariant which can be implemented in a computer algebra package. We give an example of a new invariant differing on two dessins which have the same values for the other readily computable invariants.
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Wood Melanie Matchett: Belyi-Extending Maps and the Galois Action on Dessins d’Enfants. Publ. Res. Inst. Math. Sci. 42 (2006), 721-737. doi: 10.2977/prims/1166642157