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Teichmüller curves, Galois actions and $ \widehat {GT} $ ‐relations
Author(s) -
Möller Martin
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310292
Subject(s) - mathematics , moduli space , pure mathematics , absolute galois group , teichmüller space , geodesic , space (punctuation) , action (physics) , algebraic curve , group (periodic table) , moduli of algebraic curves , galois module , mathematical analysis , riemann surface , linguistics , philosophy , physics , organic chemistry , quantum mechanics , chemistry
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)