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Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero

Benjamin Collas — 2012

Journal de Théorie des Nombres de Bordeaux

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

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