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Combinatorics of the tame automorphism group
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 145-207.

Nous étudions le groupe Tame(𝔸 3 ) des automorphismes modérés de l’espace affine de dimension 3, sur un corps de caractéristique nulle. Nous retrouvons, de manière unifiée, des résultats de Kuroda, Shestakov, Umirbaev et Wright, concernant la théorie des réductions et les relations dans Tame(𝔸 3 ). La nouveauté dans notre approche réside dans la mise en avant d’un complexe simplicial de dimension 2 simplement connexe sur lequel Tame(𝔸 3 ) agit par isométries.

We study the group Tame(𝔸 3 ) of tame automorphisms of the 3-dimensional affine space, over a field of characteristic zero. We recover, in a unified way, previous results of Kuroda, Shestakov, Umirbaev and Wright, about the theory of reduction and the relations in Tame(𝔸 3 ). The novelty in our presentation is the emphasis on a simply connected 2-dimensional simplicial complex on which Tame(𝔸 3 ) acts by isometries.

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DOI : https://doi.org/10.5802/afst.1597
@article{AFST_2019_6_28_1_145_0,
     author = {St\'ephane Lamy},
     title = {Combinatorics of the tame automorphism group},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {145--207},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 28},
     number = {1},
     year = {2019},
     doi = {10.5802/afst.1597},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1597/}
}
Stéphane Lamy. Combinatorics of the tame automorphism group. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 28 (2019) no. 1, pp. 145-207. doi : 10.5802/afst.1597. https://afst.centre-mersenne.org/articles/10.5802/afst.1597/

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