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A cohomological interpretation of the Grothendieck-Teichmüller group

with an Appendix by C. Scheiderer

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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.

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Authors and Affiliations

  1. URA 762 du CNRS, Ecole Normale Supérieure, 45 rue d’Ulm, F-75005, Paris, France

    Pierre Lochak

  2. UMR 741 du CNRS, Laboratoire de Mathématiques, Faculté des Sciences de Besançon, F-25030, Besançon Cedex, France

    Leila Schneps

  3. Fakultät für Mathematik, Universität Regensburg, D-93040, Regensburg, Germany

    C. Scheiderer

Authors
  1. Pierre Lochak
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  2. Leila Schneps
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  3. C. Scheiderer
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Oblatum 27-XI-1995

Oblatum 19-V-1996

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Lochak, P., Schneps, L. & Scheiderer, C. A cohomological interpretation of the Grothendieck-Teichmüller group. Invent. math. 127, 571–600 (1997). https://doi.org/10.1007/s002220050131

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