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Teichmüller curves, Galois actions and -relations

✍ Scribed by Martin Möller

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
298 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Teichmüller curves are geodesic discs in Teichmüller space that project to algebraic curves C in the moduli space M~g~. Some Teichmüller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group G~ℚ~ acts faithfully on the set of these embedded curves.

We also compare the action of G~ℚ~ on π~1~(C) with the one on π~1~(M~g~) 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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