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Inventiones mathematicae

, Volume 127, Issue 3, pp 571–600 | Cite as

A cohomological interpretation of the Grothendieck-Teichmüller group

with an Appendix by C. Scheiderer
  • Pierre Lochak
  • Leila Schneps
  • C. Scheiderer
Article

Abstract

In this article we interpret the relations defining the Grothendieck-Teichmüller group \(\widehat{GT}\) as cocycle relations for certain non-commutative co-homology sets, which we compute using a result due to Brown, Serre and Scheiderer. This interpretation allows us to give a new description of the elements of \(\widehat{GT}\), as well as a new proof of the Drinfel’d-Ihara theorem stating that \(\widehat{GT}\) contains the absolute Galois group
. From the same methods we deduce other properties of \(\widehat{GT}\) analogous to known properties of
, such as the self-centralizing of the complex conjugation element.

Keywords

Modulus Space Marked Point Braid Group Finite Subgroup Dehn Twist 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Pierre Lochak
    • 1
  • Leila Schneps
    • 2
  • C. Scheiderer
    • 3
  1. 1.URA 762 du CNRSEcole Normale SupérieureParisFrance
  2. 2.UMR 741 du CNRS, Laboratoire de MathématiquesFaculté des Sciences de BesançonBesançon CedexFrance
  3. 3.Fakultät für MathematikUniversität RegensburgRegensburgGermany

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