Acylindrical hyperbolicity of the three-dimensional tame automorphism group
Group Theory
2021-10-08 v2 Geometric Topology
Abstract
We prove that the group STame() of special tame automorphisms of the affine 3-space is not simple, over any base field of characteristic zero. Our proof is based on the study of the geometry of a 2-dimensional simply-connected simplicial complex C on which the tame automorphism group acts naturally. We prove that C is contractible and Gromov-hyperbolic, and we prove that Tame() is acylindrically hyperbolic by finding explicit loxodromic weakly proper discontinuous elements.
Keywords
Cite
@article{arxiv.1610.05457,
title = {Acylindrical hyperbolicity of the three-dimensional tame automorphism group},
author = {Stéphane Lamy and Piotr Przytycki},
journal= {arXiv preprint arXiv:1610.05457},
year = {2021}
}
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