Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero
Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 3, pp. 605-622.

In this paper we establish the action of the Grothendieck-Teichmüller group GT ^ on the prime order torsion elements of the profinite fundamental group π 1 geom ( 0,[n] ). As an intermediate result, we prove that the conjugacy classes of prime order torsion of π ^ 1 ( 0,[n] ) are exactly the discrete prime order ones of the π 1 ( 0,[n] ).

Cet article présente l’action du groupe de Grothendieck-Teichmüller GT ^ sur les éléments de torsion d’ordre premier du groupe fondamental profini π 1 geom ( 0,[n] ). Nous établissons par ailleurs que les classes de conjugaison d’éléments de torsion d’ordre premier de π ^ 1 ( 0,[n] ) correspondent aux classes de conjugaison discrètes de π 1 ( 0,[n] ).

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DOI: 10.5802/jtnb.813
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Benjamin Collas. Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero. Journal de Théorie des Nombres de Bordeaux, Volume 24 (2012) no. 3, pp. 605-622. doi : 10.5802/jtnb.813. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.813/

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