Teichmueller curves, Galois actions and GT-relations
Abstract
Teichmueller curves are geodesic discs in Teichmueller space that project to algebraic curves C in the moduli space Mg. Some Teichm\"uller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group G acts faithfully on the set of these embedded curves. We also compare the action of G on π1(C) with the one on π1(Mg) and obtain a relation in the Grothendieck-Teichmueller group, seemingly independent of the known ones.
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