Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Belyi-extending maps and the Galois action on dessins d'enfants   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 the ``new-type'' relations on the injection of the absolute
Galois group into the Grothendieck-Teichmuller 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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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th