Combinatorics of the tame automorphism group

Abstract

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

v4: final version, to appear in Annales de la Faculté des Sciences de Toulouse

References in corpus (4)

• Non simplicité du groupe de Cremona sur tout corps
• The tame automorphism group of an affine quadric threefold acting on a square complex
• On the acylindrical hyperbolicity of the tame automorphism group of ${\mathrm{SL}}_2(\mathbb{C})$
• Acylindrical hyperbolicity of the three-dimensional tame automorphism group

Cited by in corpus (3)

• Presqu'un immeuble pour le groupe des automorphismes modérés
• Degree growth for tame automorphisms of an affine quadric threefold
• Acylindrical hyperbolicity of the three-dimensional tame automorphism group