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Combinatorics of the tame automorphism group
Stéphane Lamy1
1 Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 28 (2019) no. 1, pp. 145-207.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1597

Stéphane Lamy 1

1 Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {Combinatorics of the tame automorphism group},
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Stéphane Lamy. Combinatorics of the tame automorphism group. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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