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

Benjamin Collas[1]

  • [1] Institut de Mathématiques de Jussieu Université Pierre et Marie Curie Paris 6 4, place Jussieu 75005 Paris

Journal de Théorie des Nombres de Bordeaux (2012)

  • Volume: 24, Issue: 3, page 605-622
  • ISSN: 1246-7405

Abstract

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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 discrete prime order ones of the π 1 ( 0 , [ n ] ) .

How to cite

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Collas, Benjamin. "Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero." Journal de Théorie des Nombres de Bordeaux 24.3 (2012): 605-622. <http://eudml.org/doc/251074>.

@article{Collas2012,
abstract = {In this paper we establish the action of the Grothendieck-Teichmüller group $\widehat\{GT\}$ on the prime order torsion elements of the profinite fundamental group $\pi _1^\{geom\}(\mathcal\{M\}_\{0,[n]\})$. As an intermediate result, we prove that the conjugacy classes of prime order torsion of $\widehat\{\pi \}_1(\mathcal\{M\}_\{0,[n]\})$ are exactly the discrete prime order ones of the $\pi _1(\mathcal\{M\}_\{0,[n]\})$.},
affiliation = {Institut de Mathématiques de Jussieu Université Pierre et Marie Curie Paris 6 4, place Jussieu 75005 Paris},
author = {Collas, Benjamin},
journal = {Journal de Théorie des Nombres de Bordeaux},
keywords = {Grothendieck-Teichmüller group; mapping class group},
language = {eng},
month = {11},
number = {3},
pages = {605-622},
publisher = {Société Arithmétique de Bordeaux},
title = {Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero},
url = {http://eudml.org/doc/251074},
volume = {24},
year = {2012},
}

TY - JOUR
AU - Collas, Benjamin
TI - Action of the Grothendieck-Teichmüller group on torsion elements of full Teichmüller modular groups in genus zero
JO - Journal de Théorie des Nombres de Bordeaux
DA - 2012/11//
PB - Société Arithmétique de Bordeaux
VL - 24
IS - 3
SP - 605
EP - 622
AB - In this paper we establish the action of the Grothendieck-Teichmüller group $\widehat{GT}$ on the prime order torsion elements of the profinite fundamental group $\pi _1^{geom}(\mathcal{M}_{0,[n]})$. As an intermediate result, we prove that the conjugacy classes of prime order torsion of $\widehat{\pi }_1(\mathcal{M}_{0,[n]})$ are exactly the discrete prime order ones of the $\pi _1(\mathcal{M}_{0,[n]})$.
LA - eng
KW - Grothendieck-Teichmüller group; mapping class group
UR - http://eudml.org/doc/251074
ER -

References

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