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Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 4, pp. 765-780.

We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.

We present examples of characters of absolute Galois groups of number fields that can be recovered through their action by automorphisms on the profinite completion of the braid groups, using a “rigidity” approach. The way we use to recover them is through classical representations of the braid groups, and in particular through the Burau representation. This enables one to extend these characters to Grothendieck-Teichmüller groups.

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DOI : https://doi.org/10.5802/afst.1202
@article{AFST_2008_6_17_4_765_0,
     author = {Ivan Marin},
     title = {Characters of the {Grothendieck-Teichm\"uller} group through rigidity of the {Burau} representation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {765--780},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 17},
     number = {4},
     year = {2008},
     doi = {10.5802/afst.1202},
     zbl = {1160.14009},
     mrnumber = {2499855},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1202/}
}
Ivan Marin. Characters of the Grothendieck-Teichmüller group through rigidity of the Burau representation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 17 (2008) no. 4, pp. 765-780. doi : 10.5802/afst.1202. https://afst.centre-mersenne.org/articles/10.5802/afst.1202/

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