Abstract
AbstractTeichmüller curves are geodesic discs in Teichmüller space that project to algebraic curves C in the moduli space Mg. Some Teichmüller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group Gℚ acts faithfully on the set of these embedded curves.We also compare the action of Gℚ on π1(C) with the one on π1(Mg) and obtain a relation in the Grothendieck–Teichmüller group, seemingly independent of the known ones. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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